title: Tensor Charge of the Nucleon in Lattice QCD

abstract:
  First results of lattice QCD simulation on the nucleon tensor-charge $\delta
q$ are presented. From the quenched QCD simulations with the Wilson quark
action at $\beta = 5.7$ on a 16$^3\times$ 20 lattice and on a $12^3\times 20$
lattice, we find (i) the connected part $\delta q_{con.}$ is determined with
small statistical error, (ii) the disconnected part $\delta q_{dis.}$, which
violates the OZI rule, is consistent with zero, and (iii) the flavor-singlet
tensor charge $ \delta \Sigma (\mu^2 = 2 {\rm GeV}^2) = \delta u + \delta d +
\delta s$ takes 0.562(88) at $\beta=5.7$, which is in contrast with the
flavor-singlet axial charge $\Delta \Sigma = 0.1-0.3$.


title: A Gauge-Fixing Action for Lattice Gauge Theories

abstract:
  We present a lattice gauge-fixing action $S_{gf}$ with the following
properties: (a) $S_{gf}$ is proportional to the trace of $(\sum_\mu
\partial_\mu A_\mu)^2$, plus irrelevant terms of dimension six and higher; (b)
$S_{gf}$ has a unique absolute minimum at $U_{x,\mu}=I$. Noting that the
gauge-fixed action is not BRST invariant on the lattice, we discuss some
important aspects of the phase diagram.


title: Lattice Chiral Gauge Theories in a Renormalizable Gauge

abstract:
  The lattice formulation of gauge theories in a renormalizable gauge is
discussed. The formulation invokes a new phase diagram, and it may allow for a
lattice definition of Chiral Gauge Theories.


title: The 3-loop Beta Function of QCD

abstract:
  Using the background field technique, we calculate the 3-loop beta function
of lattice $SU(N)$ gauge theories. In the pure gluonic case, we present our
results, comparing to those recently obtained by Luescher and Weisz. We also
provide a progress report in the case of QCD with Wilson fermions.


title:
On Existence of Nontrivial Fixed Points in Large $N$ Gauge Theory in
  More than Four Dimensions

abstract:
  Inspired by a possible relation between large $N$ gauge theory and string
theory, we search for nontrivial fixed points in large $N$ gauge theory in more
than four dimensions. We study large $N$ gauge theory through Monte Carlo
simulation of the twisted Eguchi-Kawai model in six dimensions as well as in
four dimensions. The phase diagram of the system with the two coupling
constants which correspond to the standard plaquette action and the adjoint
term has been explored.


title: Can we do better than Hybrid Monte Carlo in Lattice QCD?

abstract:
  The Hybrid Monte Carlo algorithm for the simulation of QCD with dynamical
staggered fermions is compared with Kramers equation algorithm. We find
substantially different autocorrelation times for local and nonlocal
observables. The calculations have been performed on the parallel computer CRAY
T3D.


title:
Blockspin transformation for finite temperature field theories with
  gauge fields

abstract:
  A procedure is proposed to study QFT at zero or at finite temperature by a
sequence of real space renormalization group (RG) or blockspin transformations.
They transform to effective theories on coarser and coarser lattices.The
ultimate aim is to compute constraint effective potentials, i.e. the free
energy as a function of suitable order parameters.From the free energy one can
read off the thermodynamic behaviour of the theory, in particular the existence
and nature of phase transitions. In a finite temperature QFT one begins with
either one or a sequence of transformations which transform the original theory
into an effective theory on a three-dimensional lattice. Its effective action
has temperature dependent coefficients. Thereafter one may proceed with further
blockspin transformations of the three-dimensional theory. Assuming a finite
volume, this can in principle be continued until one ends with a lattice with a
single site. Its effective action is the constraint effective potential. In
each RG-step, an integral over the high frequency part of the field has to be
performed. This is done perturbatively and requires the knowledge of bare
fluctuation field propagators and of interpolation operators which enter into
the vertices. A detailed examination of these quantities is presented for
scalar fields, abelian gauge fields and for Higgs fields, finite temperature is
admitted.


title: Electroweak phase transition by four dimensional simulations

abstract:
  The finite temperature phase transition in the SU(2)-Higgs model at a Higgs
boson mass $M_H \simeq 35$ GeV is studied in numerical simulations on four
dimensional lattices with time-like extensions up to $L_t=5$. $T_c/M_H$ is
extrapolated to the continuum limit and a comparison with the perturbative
prediction is made. A one-loop calculation to the coupling anisotropies of the
SU(2)-Higgs model on lattices with asymmetric lattice spacings is presented.
Our numerical simulations show that the above perturbative result is applicable
in the phenomenologically interesting parameter region.


title: Decorrelating the topology in full QCD

abstract:
  We investigate the performance of the hybrid Monte Carlo algorithm in
updating non-trivial global topological structures. We find that the hybrid
Monte Carlo algorithm has serious problems decorrelating the global topological
charge. This represents a warning which must be seriously considered when
simulating full QCD, regardless of the number and type of fermions, with this
or any similar algorithm. Simulated tempering is examined as a means of
accelerating the decorrelation.


title:
Non-Perturbative Renormalization of the Lattice Heavy Quark Classical
  Velocity

abstract:
  We discuss the renormalization of the lattice formulation of the Heavy Quark
Effective Theory (LHQET). In addition to wave function and composite operator
renormalizations, on the lattice the classical velocity is also renormalized.
The origin of this renormalization is the reduction of Lorentz (or O(4))
invariance to (hyper)cubic invariance. We present results of a new, direct
lattice simulation of this finite renormalization, and compare the results to
the perturbative (one loop) result. The simulation results are obtained with
the use of a variationally optimized heavy-light meson operator, using an
ensemble of lattices provided by the Fermilab ACP-MAPS collaboration.


title: Phase structure of QCD for general number of flavors

abstract:
  We investigate and elucidate the phase structure of QCD for general number of
flavors $N_F$ with Wilson quarks, varying $N_F$ from 2 up to 300. Based on
numerical results combined with the result of the perturbation theory we
propose the following picture: When $N_F \ge 17$, there is only a trivial fixed
point and therefore the theory in the continuum limit is trivial. On the other
hand, when $16 \ge N_F \ge 7$, there is a non-trivial fixed point and therefore
the theory is non-trivial with anomalous dimensions, however, without quark
confinement. Theories which satisfy both quark confinement and spontaneous
chiral symmetry breaking in the continuum limit exist only for $N_F \le 6$. We
also discuss the structure of the deconfining phase at finite temperatures for
the small number of flavors such as $N_F=2$ and 3, through a systematic study
of it for general number of flavors.


title: Hodge gauge fixing in three dimensions

abstract:
  A progress report on experiences with a gauge fixing method proposed in
LATTICE 94 is presented. In this algorithm, an SU(N) operator is diagonalized
at each site, followed by gauge fixing the diagonal (Cartan) part of the links
to Coulomb gauge using the residual abelian freedom. The Cartan sector of the
link field is separated into the physical gauge field $\alpha^{(f)}_\mu$
responsible for producing $f^{\rm Cartan}_{\mu\nu}$, the pure gauge part,
lattice artifacts, and zero modes. The gauge transformation to the physical
gauge field $\alpha^{(f)}_\mu$ is then constructed and performed. Compactness
of the lattice fields entails issues related to monopoles and zero modes which
are addressed.


title: Simulating QCD at finite density with static quarks

abstract:
  We study lattice QCD in the limit that the quark mass and chemical potential
are simultaneously made large, resulting in a controllable density of quarks
which do not move; this is similar in spirit to the quenched approximation for
zero density QCD. In this approximation we find that the deconfinement
transition seen at zero density becomes a smooth crossover for any nonzero
density at which we simulated, and that at low enough temperature chiral
symmetry remains broken at all densities.


title: Manifestations of the axial anomaly in finite temperature QCD

abstract:
  We compute the flavor singlet meson correlators and screening masses in
quenched and $N_f=2$ QCD at $N_t=8$. The consequences of our results for the
realization of the $U_A(1)$ symmetry at finite T are discussed and an
interpretation of our measurements in terms of the behaviour of the low lying
fermionic modes is proposed.


title: Monopole action and monopole condensation in SU(3) lattice QCD

abstract:
  Effective monopole actions for various extended monopoles are derived from
vacuum configurations after abelian projection in the maximally abelian gauge
in $T=0$ and $T\ne 0$ $SU(3)$ lattice QCD. The actions obtained appear to be
independent of the lattice volume adopted. At zero temperature, monopole
condensation is seen to occur from energy-entropy balance in the strong
coupling region.
  Larger $\beta$ is included in the monopole condensed phase as more extended
monopoles are considered. The scaling seen in the $SU(2)$ case is not yet
observed. The renormalization flow diagram suggests the existence of an
infrared fixed point. A hysteresis behavior is seen around the critical
temperature in the case of the $T\ne 0$ action.


title: Pomerons and Lattices: a Progress Report

abstract:
  We report on some attempts to use lattice QCD to investigate topics in strong
interactions phenomenology which are usually interpreted in terms of soft
Pomeron exchange.


title: A New Lattice Action for Studying Topological Charge

abstract:
  We review our recent proposal for a new lattice action for non-abelian gauge
theories which reduces short-range lattice artifacts in the computation of the
topological susceptibility. The standard Wilson action is replaced by the
Wilson action of a gauge covariant interpolation of the original fields to a
finer lattice. We illustrate the improved behavior of a same-philosophy new
lattice action in the $O(3)$ $\sigma$-model in two dimensions.


title: Lattice Gauge Field Interpolation for Chiral Gauge Theories

abstract:
  The importance of lattice gauge field interpolation for our recent
non-perturbative formulation of chiral gauge theory is emphasized. We
illustrate how the requisite properties are satisfied by our recent
four-dimensional non-abelian interpolation scheme, by going through the simpler
case of U(1) gauge fields in two dimensions.


title: Critical exponents and abelian dominance in $SU(2)$ QCD

abstract:
  The critical properties of the abelian Polyakov loop and the Polyakov loop in
terms of Dirac string are studied in finite temperature abelian projected
$SU(2)$ QCD. We evaluate the critical point and the critical exponents from
each Polyakov loop in the maximally abelian gauge using the finite-size scaling
analysis. Abelian dominance in this case is proved quantitatively. The critical
point of each abelian Polyakov loop is equal to that of the non-abelian
Polyakov loop within the statistical errors. Also, the critical exponents are
in good agreement with those from non-abelian Polyakov loops.


title:
Toward the Continuum Limit of $B_K$ with the Quenched Kogut-Susskind
  Quark Action

abstract:
  We present new results of our ongoing project toward a precision
determination of the kaon $B$ parameter with the Kogut-Susskind quark action in
quenched QCD. New results taken at $\beta$=6.4 and $\beta=5.7$ suggest that an
apparently linear $a$ dependence of $B_K$ previously observed for
$\beta=5.85-6.2$ arises from a change of curvature from convex to concave as
the lattice spacing is reduced. Fitting data for $\beta\geq 5.93$ with an
$O(a^2)$ form yields $B_K$(NDR,2 GeV)=0.587(7)(17) in the continuum limit. We
also describe a finite-size study of $B_K$ at $\beta=$ 6.0 and 6.4, and a
reanalysis of the theoretical argument for $O(a^2)$ behavior.


title: Calculation of the renormalized charmed-quark mass in Lattice QCD

abstract:
  The correlator of heavy-quark currents is calculated in quenched Lattice QCD
on a $16^3 \times 32$-lattice for $\beta= { 6, 6.3 }$. The renormalized charmed
quark mass is extracted from the short-distance part of that correlator:
$m_c^{\overline{MS}}(m_c) = 1.22(5) GeV$. We study the sensitivity of our data
to the strong coupling constant.


title: Gribov Copy and Complex Phase of Chiral Determinant

abstract:
  We calculate the complex phase of chiral determinant by the vacuum overlap
formula with configurations of two-dimensional U(1) gauge field fixed in Landau
and Laplacian gauge. The complex phase fluctuates over the Gribov copies, which
appear in the process of Landau gauge fixing and contain vortex-like
singularities. In the Laplacian gauge, the fluctuation can be reduced and the
phase can be determined uniquely. If it is used as a preconditioning for Landau
gauge fixing, the most smooth configuration is obtained among the copies
generated.


title: Wess-Zumino term by Vacuum Overlap Formula

abstract:
  We examine the vacuum overlap formula for the two-dimensional SU(2)
Wess-Zumino term in lattice regularization. Perturbatively it reproduces the
Wess-Zumino term correctly in the continuum limit and yields the IR fixed point
in the beta function of the chiral model. Nonperturbatively it shows a sharp
Gaussian distribution for the SU(2) chiral field configurations in the scaling
region, where smooth configurations dominate even in the symmetric phase due to
asymptotic freedom. Crossover is sharp from the strong coupling region where
the Wess-Zumino term fluctuates hard and the species doublers' contribution is
suspected to affect it.


title:
Comment on "The two-phase issue in the O(n) non-linear sigma-model: a
  Monte-Carlo study" by B.Alles, A.Buonanno and G.Cella

abstract: We comment on the recent paper by Alles et al (hep-lat/9608002)


title: Binding Energies in Nonrelativistic Field Theories

abstract:
  Relativistic corrections communicate the binding energy of a bound state to
its kinetic mass. This mechanism is reviewed and used to explain anomalous
results of Collins, Edwards, Heller, and Sloan (hep-lat/9512026), which
compared rest and kinetic masses of heavy-light mesons and quarkonia.


title: Staggered fermions and their $O(a)$ improvements

abstract:
  Expanding upon the arguments of Sharpe, we explicitly implement the Symanzik
improvement program demonstrating the absence of order $a$ terms in the
staggered fermion action. We propose a general program to improve fermion
operators to remove $O(a)$ corrections from their matrix elements, and
demonstrate this program for the examples of matrix elements of fermion
bilinears and $B_K$. We also determine the additional operators which must be
added to improve the staggered fermion currents.


title:
SU(3) Latent Heat and Surface Tension from Tree Level and Tadpole
  Improved Actions

abstract:
  We analyze the latent heat and surface tension at the SU(3) deconfinement
phase transition with tree level and tadpole improved Symanzik actions on
lattices with temporal extent $N_\tau = 3$ and 4 and spatial extent $N_\sigma/
N_\tau = 4$, 6 and 8. In comparison to the standard Wilson action we do find a
drastic reduction of cut-off effects already with tree level improved actions.
On lattices with temporal extent $N_\tau=4$ results for the surface tension and
latent heat obtained with a tree level improved action agree well with those
obtained with a tadpole improved action. A comparison with $N_\tau=3$
calculations, however, shows that results obtained with tadpole action remain
unaffected by cut-off effects even on this coarse lattice, while the tree level
action becomes sensitive to the cut-off. For the surface tension and latent
heat we find $\sigma_I/ T_c^3 = 0.0155~(16)$ and $\Delta\epsilon/T_c^4 =
1.40~(9)$, respectively.


title:
Continuum Limit of the Heavy-Light Decay Constant with the Quenched
  Wilson Quark Action

abstract:
  We explore the problems in calculating the decay constant for heavy-light
mesons using the quenched Wilson quark action for both heavy and light quarks.
We find that the continuum limit of the decay constant is reasonably converged
among different prescriptions after the continuum limit is taken. A number of
technical problems associated with prescriptions are also addressed.


title: Electromagnetic Structure of Light Baryons in Lattice QCD

abstract:
  A method in which electromagnetic properties of hadrons are studied by direct
simulation of dynamical photon effects is applied to the extraction of the
isomultiplet structure of the octet baryons. Using 187 configurations at
$\beta=5.7$ with Wilson action, and up and down quark masses determined from
the meson spectrum, the nucleon splitting is found to be $1.55(\pm 0.56\; \rm
stat)$ MeV; the hyperon splittings are found to be
$\Sigma^{0}-\Sigma^{+}=2.47\pm 0.39$, $\Sigma^{-}-\Sigma^{0}=4.63\pm 0.36$,
$\Xi^{-}-\Xi^{0}=5.68\pm 0.24$ MeV. Estimated systematic corrections arising
from finite volume and the quenched approximation are included in these
results.


title: Topics in Light Hadron Mass Spectrum in Quenched QCD

abstract:
  Several topics concerning the light hadron spectrum are discussed. Flavor
symmetry breaking effects and the problem of quenched chiral logarithm are
examined with pion mass data for the Kogut-Susskind quark action, and light
meson decay constants for the Wilson action calculated with non-perturbative
renormalization constants are discussed. Results for quark masses are also
given both for the Kogut-Susskind and Wilson actions.


title: Approximate Actions for Lattice QCD Simulation

abstract:
  We describe a systematic approach to generating approximate actions for the
lattice simulation of QCD. Three different tuning conditions are defined to
match approximate with true actions, and it is shown that these three
conditions become equivalent when the approximate and true actions are
sufficiently close. We present a detailed study of approximate actions in the
lattice Schwinger model together with an exploratory study of full QCD at
unphysical parameter values. We find that the technicalities of the approximate
action approach work quite well. However, very delicate tuning is necessary to
find an approximate action which gives good predictions for all physical
observables. Our best view of the immediate applicability of the methods we
describe is to allow high statistics studies of particular physical observables
after a low statistics full fermion simulation has been used to prepare the
stage.


title: Square Symanzik action to one-loop order

abstract:
  We present the one-loop coefficients for an alternative Symanzik improved
lattice action with gauge groups SU(2) or SU(3).


title:
Continuum extrapolation of energies of a four-quark system in lattice
  gauge theory

abstract:
  A continuum extrapolation of static two- and four-quark energies calculated
in quenched SU(2) lattice Monte Carlo is carried out based on Sommer's method
of setting the scale. The beta-function is obtained as a side product of the
extrapolations. Four-quark binding energies are found to be essentially
constant at beta >= 2.35 unlike the two-body potentials. A model for four-quark
energies, with explicit gluonic degrees of freedom removed, is fitted to these
energies and the behaviour of the parameters of the model is investigated. An
extension of the model using the first excited states of the two-body gluon
field as additional basis states is found to be necessary for quarks at the
corners of regular tetrahedra.


title: Status of the CP-PACS Project

abstract:
  The CP-PACS computer with a peak speed of 300 Gflops was completed in March
1996 and has started to operate. We describe the final specification and the
hardware implementation of the CP-PACS computer, and its performance for QCD
codes. A plan of the grade-up of the computer scheduled for fall of 1996 is
also given.


title: Scaling Structures in Four-dimensional Simplicial Gravity

abstract:
  Four-dimensional(4D) spacetime structures are investigated using the concept
of the geodesic distance in the simplicial quantum gravity. On the analogy of
the loop length distribution in 2D case, the scaling relations of the boundary
volume distribution in 4D are discussed in various coupling regions i.e.
strong-coupling phase, critical point and weak-coupling phase. In each phase
the different scaling relations are found.


title:
B_K with the Wilson Quark Action: A Non-Perturbative Resolution of
  Operator Mixing using Chiral Ward Identities

abstract:
  We propose a non-perturbative method to determine the mixing coefficients of
$\Delta s=2$ four-quark operators for the Wilson quark action using chiral Ward
identities. The method is applied to calculate B_K in quenched QCD.


title: Fixed versus random triangulations in 2D simplicial Regge calculus

abstract:
  We study 2D quantum gravity on spherical topologies using the Regge calculus
approach with the $dl/l$ measure. Instead of a fixed non-regular triangulation
which has been used before, we study for each system size four different random
triangulations, which are obtained according to the standard Voronoi-Delaunay
procedure. We compare both approaches quantitatively and show that the
difference in the expectation value of $R^2$ between the fixed and the random
triangulation depends on the lattice size and the surface area $A$. We also try
again to measure the string susceptibility exponents through a finite-size
scaling Ansatz in the expectation value of an added $R^2$ interaction term in
an approach where $A$ is held fixed. The string susceptibility exponent
$\gamma_{str}'$ is shown to agree with theoretical predictions for the sphere,
whereas the estimate for $\gamma_{str}$ appears to be too negative.


title: Dynamical Fermion on Random-Block Lattice

abstract:
  Massless fermion field interacting with abelian dynamical gauge field on
2-dimensional random-block lattices are investigated using Hybrid Monte Carlo
simulations. Preliminary results of the Wilson loop and the chiral correlation
function are in agreement with the continuum Schwinger model.


title: Complex structure of a DT surface with $T^2$ topology

abstract:
  A method of defining the complex structure(moduli) for dynamically
triangulated(DT) surfaces with torus topology is proposed. Distribution of the
moduli parameter is measured numerically and compared with the Liouville theory
for the surface coupled to c = 0, 1 and 2 matter. Equivalence between the
dynamical triangulation and the Liouville theory is established in terms of the
complex structure.


title: The large-N expansion of unitary-matrix models

abstract:
  The general features of the 1/N expansion in statistical mechanics and
quantum field theory are briefly reviewed both from the theoretical and from
the phenomenological point of view as an introduction to a more detailed
analysis of the large-N properties of spin and gauge models possessing the
symmetry group $SU(N) \times SU(N)$.
  An extensive discussion of the known properties of the single-link integral
(equivalent to YM_2 and one-dimensional chiral models) includes finite-$N$
results, the external field solution, properties of the determinant, and the
double scaling limit.
  Two major classes of solvable generalizations are introduced: one-dimensional
closed chiral chains and models defined on a $d-1$ dimensional simplex. In both
cases large-N solutions are presented with emphasis on their double scaling
properties.
  The available techniques and results concerning unitary-matrix models that
correspond to asymptotically free quantum field theories (two-dimensional
chiral models and four-dimensional QCD) are discussed, including
strong-coupling methods, reduced formulations, and the Monte Carlo approach.


title: Deconfinement from Action Restriction

abstract:
  The effect of restricting the plaquette to be greater than a certain cutoff
value is studied. The action considered is the standard Wilson action with the
addition of a plaquette restriction, which should not affect the continuum
limit of the theory. In this investigation, the strong coupling limit is also
taken. It is found that a deconfining phase transition occurs as the cutoff is
increased, on all lattices studied (up to $20^4$). The critical cutoff on the
infinite lattice appears to be around 0.55. For cutoffs above this, a fixed
point behavior is observed in the normalized fourth cumulant of the Polyakov
loop, suggesting the existence of a line of critical points corresponding to a
massless gluon phase, not unlike the situation in compact U(1). The Polyakov
loop susceptibility also appears to be diverging with lattice size at these
cutoffs. A strong finite volume behavior is observed in the pseudo-specific
heat. It is discussed whether these results could still be consistent with the
standard crossover picture which precludes the existence of a deconfining phase
transition on an infinite symmetric lattice.


title:
SU(3) Flavor Breaking in Hadronic Matrix Elements for $B - \bar B$
  Oscillations

abstract:
  We present an analysis, using quenched configurations at $6/g^2=$5.7, 5.85,
6.0, and 6.3 of the matrix element $\MP\equiv\langle \bar P_{hl}|\bar h
\gamma_\mu (1-\gamma_5)l \bar h \gamma_\mu(1-\gamma_5)l|P_{hl}\rangle$ for
heavy-light pseudoscalar mesons. The results are extrapolated to the physical
$B$ meson states, $\Bd$ and $\Bs$. We directly compute the ratio $\MS/\MB$, and
obtain the preliminary result $\MS/\MB=1.54(13)(32)$. A precise value of this
SU(3) breaking ratio is important for determining $V_{td}$ once the mixing
parameter $x_s$ for $\Bs-\bar\Bs$ is measured experimentally. We also determine
values for the corresponding B parameters, $B_{bs}(2 \rm{GeV})=B_{bd}(2
\rm{GeV})=1.02(13)$, which we cannot distinguish in the present analysis.


title: On the Nf and a Dependence of BK

abstract:
  We present results of a study of BK using tadpole improved gauge invariant
staggered operators. Using three ensembles of 16^3x32 configurations with
varying numbers of dynamical flavors, we observe a small dependence on Nf.
Using seven quenched ensembles between beta=5.7 and beta=6.2 we extrapolate to
a=0.


title: The Staggered Eta-prime with Smeared Operators

abstract:
  We present a refined calculation of the eta-prime mass using staggered
fermions and Wuppertal smeared operators. We use quenched and dynamical
configurations of size 16^3x32 with Nf=0, Nf=2 and Nf=4, and compare our
results with the expected forms from quenched, partially quenched and
unquenched chiral perturbation thoery.


title:
The Light Hadron Mass Spectrum with Non-Perturbatively O(a) Improved
  Wilson Fermions

abstract:
  We compute the light hadron mass spectrum in quenched lattice QCD at $\beta =
6.0$ using the Sheikholeslami-Wohlert fermionic action. The calculation is done
for several choices of the coefficient $c_{SW}$, including $c_{SW} = 0$ and the
recently proposed optimal value $c_{SW} = 1.769$. We find that the individual
masses change by up to 30\% under $O(a)$ improvement. The spectrum calculation
suggests $c_{SW} \approx 1.4$ for the optimal value of the coefficient.


title:
Domain-wall fermions with U(1) dynamical gauge fields in
  (4+1)-dimensions

abstract:
  We carry out a numerical simulation of a domain-wall model in (4+1)
dimensions, in the presence of a quenched U(1) dynamical gauge field only in an
extra dimension, corresponding to the weak coupling limit of a (4-dimensional)
physical gauge coupling. Our numerical data suggest that the zero mode seems
absent in the symmetric phase, so that it is difficult to construct a lattice
chiral gauge theory in the continuum limit.


title: APEmille: a parallel processor in the teraflop range

abstract:
  APEmille is a SIMD parallel processor under development at the Italian
National Institute for Nuclear Physics (INFN). APEmille is very well suited for
Lattice QCD applications, both for its hardware characteristics and for its
software and language features. APEmille is an array of custom arithmetic
processors arranged on a tridimensional torus. The replicated processor is a
pipelined VLIW device performing integer and single/double precision IEEE
floating point operations. The processor is optimized for complex computations
and has a peak performance of 528Mflop at 66MHz and of 800Mflop at 100MHz. In
principle an array of 2048 nodes is able to break the Tflops barrier. A
powerful programming language named TAO is provided and is highly optimized for
QCD. A C++ compiler is foreseen. Specific data structures, operators and even
statements can be defined by the user for each different application. Effort
has been made to define the language constructs for QCD.


title: DIS Structure Functions in Lattice QCD

abstract:
  In this talk I present the complete 1-loop perturbative computation of the
renormalization constants and mixing coefficients of quark and gluon lattice
operators of rank two and three whose hadronic elements enter in the
determination of the first and second moment of Deep Inelastic Scattering
Structure Functions, making use of the nearest-neighbor improved
``clover-leaf'' lattice QCD action.
  To perform the huge amount of calculations required for the evaluation of all
the relevant Feynman diagrams, extensive use of symbolic manipulation languages
like Schoonschip and Form has been made.


title: Effect of Improving the Lattice Gauge Action on QCD Topology

abstract:
  We use lattice topology as a laboratory to compare the Wilson action (WA)
with the Symanzik-Weisz (SW) action constructed from a combination of (1x1) and
(1x2) Wilson loops, and the estimate of the renormalization trajectory (RT)
from a renormalization group transformation (RGT) which also includes higher
representations of the (1x1) loop. Topological charges are computed using the
geometric (L\"uscher's) and plaquette methods on the uncooled lattice, and also
by using cooling to remove ultraviolet artifacts. We show that as the action
improves by approaching the RT, the topological charges for individual
configurations computed using these three methods become more highly
correlated, suggesting that artificial lattice renormalizations to the
topological susceptibility can be suppressed by improving the action.


title: Exact Local Bosonic Algorithm for Dynamical Quarks

abstract:
  We present an exact local bosonic algorithm for the simulation of dynamical
fermions in lattice QCD. We show that this algorithm is a viable alternative to
the Hybrid Monte Carlo algorithm.


title: Light Quark Masses with an O(a)-Improved Action

abstract:
  We present the recent Fermilab calculations of the masses of the light
quarks, using tadpole-improved Sheikholeslami-Wohlert (SW) quarks. Various
sources of systematic errors are studied. Our final result for the average
light quark mass in the quenched approximation evaluated in the $\bar{MS}$
scheme is $\bar{m}_q(\mu=2 GeV;n_f=0)= (m_u+m_d)/2=3.6 \pm 0.6 MeV$.


title: Electromagnetic Splittings and Light Quark Masses

abstract:
  A method for computing electromagnetic properties of hadrons in lattice QCD
is described. The electromagnetic field is introduced dynamically, using a
noncompact formulation. Employing enhanced electric charges, the dependence of
the pseudoscalar meson mass on the (anti)quark charges and masses can be
accurately calculated. At $\beta=5.7$ with Wilson action, the $\pi^+-\pi^0$
splitting is found to be $4.9(3)$ MeV. Using the measured $K^0-K^+$ splitting,
we also find $m_u/m_d = .512(6)$. Systematic errors are discussed. Preliminary
results for vector meson splittings are also presented.}


title:
Monopoles and the Chiral Phase Transition in $SU(2)$ Lattice Gauge
  Theory

abstract:
  In the quenched approximation we use the abelian and monopole fields from
abelian projection in SU(2) lattice gauge theory to numerically compute the
value of the chiral condensate. The condensate calculated using abelian
projection is observed to vanish at the same critical temperature as the full
SU(2) theory predicts.


title: Light Quenched Hadron Spectrum and Decay Constants on different Lattices

abstract:
  We present a study of ${\cal O}(2000)$ (quenched) lattice configurations from
the APE collaboration, for $6.0\le\beta\le 6.4$ using both the Wilson and the
SW-Clover fermion action. We determine the light hadronic spectrum and meson
decay constants. We extract the inverse lattice spacing using data at the
simulated values of the quark mass. We find an agreement with the experimental
data of $\sim 5%$ for mesonic masses and $\sim 10%-15%$ for baryonic masses and
pseudoscalar decay constants. A larger deviation is present for the vector
decay constants.


title: Parton Distribution Functions

abstract:
  Parton distribution functions give the probability to find partons (quarks
and gluons) in a hadron as a function of the fraction x of the proton's
momentum carried by the parton. They are conventionally defined in terms of
matrix elements of certain operators. They are determined from experimental
results on short distance scattering of the partons. Integrals of these
functions weighted with x^n are calculable using lattice QCD. Some simple
models for their behavior have implications that could also be tested in
lattice QCD.


title: Sum rules and 2-quark flux-tube structure

abstract:
  Sum rules -- relating the static quark potential V(R) to the spatial
distribution of the action and energy in the colour fields of flux-tubes -- are
applied in three ways: 1) To extract generalised beta-functions: 2) As a
consistency check for the use of excited gluon flux-tubes and as an estimate of
the quark self-energies: 3) To extract approximate sum rules using a simplified
form of V(R). Also the flux-tube profiles are compared with hadronic string and
flux-tube models.


title: Recent Results on the Abelian Projection of Lattice Gluodynamics

abstract:
  The abelian projection of lattice gluodynamics is reviewed. The main topics
are: abelian and monopole dominance, monopole condensate as the disorder
parameter, effective abelian Lagrangian, monopoles in the instanton field,
Aharonov -- Bohm effect on the lattice.


title: Finite Temperature Gauge Theory on Anisotropic Lattices

abstract:
  The finite temperature transition of QCD can be seen as a change in the
structure of the hadrons and as a symmetry breaking transition -- a change in
the structure of the vacuum. These phenomena are observed differently and carry
complementary information. We aim at a correlated analysis involving hadronic
correlators and the vacuum structure including field and density correlations,
both non-trivial questions.


title: Scaling of Chiral Order Parameter in Two-Flavor QCD

abstract:
  The finite temperature transition of QCD with two degenerate light quarks is
studied on the lattice with a renormalization group improved gauge action and
the Wilson quark action. We have made simulations on an $8^3\times 4$ lattice
near the chiral transition point. It is shown that the chiral condensate which
is the order parameter of chiral symmetry satisfies remarkably a scaling
relation with the exponents of the three dimensional O(4) Heisenberg model.
This indicates that the chiral transition in two-flavor QCD is of second order
in the continuum limit.


title: Quenched KS light hadron mass at \beta=6.5 on a 64\times 48^3 lattice

abstract:
  We report our quenched staggered light hadron mass calculation at the
coupling of \beta = 6.5 on a 48^3 \times 64 lattice, based on an increased
statistics of two hundred gauge configurations. Staggered quark wall sources
with mass of m_q a = 0.01, 0.005, 0.0025 and 0.00125 are used. Flavor symmetry
is restored for pion and \rho meson. The lattice scale is estimated to be
a^{-1} = 3.7(2) GeV.


title:
Reply to A. Patrascioiu's and E. Seiler's comment on our paper "The
  two-phase issue in the O(n) non-linear sigma-model: a Monte Carlo study"

abstract:
  We reply to a comment by A. Patrascioiu and E. Seiler appeared in
hep-lat/9608138 on our paper hep-lat/9608002.


title: The three-loop beta function in SU(N) lattice gauge theories

abstract:
  We calculate the third coefficient of the lattice $\beta$ function in pure
Yang-Mills theory. We make use of a computer code for solving perturbation
theory analytically on the lattice. We compute the divergent integrals by using
a method based on a Taylor expansion of the integrand in powers of the external
momenta in $4 - \epsilon$ dimensions. Our results are in agreement with a
previous calculation by M. L\"uscher and P. Weisz where the authors used a
different technique. We also show how this new coefficient modifies the scaling
function on the lattice in both the standard and energy schemes. In particular
we show that asymptotic scaling is extremely well achieved in the energy
scheme.


title: Nature of the Vacuum inside the Color Flux Tube

abstract:
  The interior of the color flux tube joining a quark pair can be probed by
evaluating the correlator of pair of Polyakov loops in a vacuum modified by
another Polyakov pair, in order to check the dual superconductivity conjecture
which predicts a deconfined, hot core. We also point out that at the critical
point of any 3D gauge theories with a continuous deconfining transition the
Svetitsky-Yaffe conjecture provides us with an analytic expression of the
Polyakov correlator as a function of the position of the probe inside the flux
tube. Both these predictions are compared with numerical results in 3D Z2 gauge
model finding complete agreement.


title: Effective actions for finite temperature Lattice Gauge Theories

abstract:
  We consider a lattice gauge theory at finite temperature in ($d$+1)
dimensions with the Wilson action and different couplings $\beta_t$ and
$\beta_s$ for timelike and spacelike plaquettes. By using the character
expansion and Schwinger-Dyson type equations we construct, order by order in
$\beta_s$, an effective action for the Polyakov loops which is exact to all
orders in $\beta_t$. As an example we construct the first non-trivial order in
$\beta_s$ for the (3+1) dimensional SU(2) model and use this effective action
to extract the deconfinement temperature of the model.


title:
Full QCD with dynamical Wilson fermions on a 24^3 x 40-lattice -- a
  feasibility study

abstract:
  The investigation of light sea-quark effects in lattice QCD with dynamical
Wilson fermions requires both larger physical volumes and finer lattice
resolutions than achieved previously. As high-end supercomputers like the
512-node APE Tower provide the compute power to perform a major step towards
the chiral limit (T-chi-L), we have launched a feasibility study on a 24^3 x 40
lattice. We approach the chiral limit--while refining the resolution--, using
the standard Wilson fermion action. Following previous work, our Hybrid Monte
Carlo simulation runs at beta=5.6 and two kappa-values, 0.1575 and 0.158. From
our study, we are confident that, for the APE Tower, a realistic working point
has been found corresponding to a volume of 2 fm^3, with chirality
characterized by 1/(a m_pi) = 5.6.


title: Chiral Perturbation Theory and Weak Matrix Elements

abstract:
  I describe recent developments in quenched chiral perturbation theory (QChPT)
and the status of weak matrix elements involving light quarks. I illustrate
how, with improved statistical errors, and with calculations of the masses of
baryons containing non-degenerate quarks, there is now a clear need for
extrapolations of higher order than linear in the quark mass. I describe how
QChPT makes predictions for the functional forms to use in such extrapolations,
and emphasize the distinction between contributions coming from chiral loops
which are similar to those present in unquenched theories, and those from
$\eta'$ loops which are pure quenched artifacts. I describe a fit to the baryon
masses using the predictions of QChPT. I give a status report on the numerical
evidence for $\eta'$ loops, concluding that they are likely present, and are
characterized by a coupling $\delta=0.1-0.2$. I use the difference between
chiral loops in QCD and quenched QCD to estimate the quenching errors in a
variety of quantities. I then turn to results for matrix elements, largely from
quenched simulations. Results for quenched decay constants cannot yet be
reliably extrapolated to the continuum limit. By contrast, new results for
$B_K$ suggest a continuum, ``quenched'' value of $B_K(NDR, 2 GeV) = 0.5977 \pm
0.0064 \pm 0.0166$, based on a quadratic extrapolation in $a$. The theoretical
basis for using a quadratic extrapolation has been confirmed. For the first
time there is significant evidence that unquenching changes $B_K$, and my
estimate for the value in QCD is $B_K(NDR, 2 GeV) = 0.66 \pm 0.02 \pm 0.11$.
Here the second error is a conservative estimate of the systematic error due to
uncertainties in the effect of quenching. A less conservative viewpoint reduces
$0.11$ to $0.03$.


title:
New Universality Classes in One--Dimensional $O(N)$--Invariant
  Spin--Models with an $n$--Parametric Action

abstract:
  An action with $n$ parameters, which generalizes the $O(N) - R P^{N-1}$
-model, is considered in one dimension for general $N$. We use asymptotic
expansion techniques to determine where the model becomes critical and show
that for the actions considered there exists a family of hypersurfaces whose
asymptotic behaviour determines a one-parameter family of new universality
classes. They interpolate between the $O(N)$-vector-model-class and the $R
P^{N-1}$-model-class. Furthermore continuum limits are discussed, including the
exceptional case $N=2$.


title: Massless Composite Fermions in Two Dimensions and the Overlap

abstract:
  There exist chiral gauge models in two dimensions that have massless
composite fermions. Two examples are presented and it is suggested that they be
accepted as benchmark test-cases for generic proposals of non-perturbatively
regulating chiral gauge theories in any dimension. We apply the overlap to the
simpler of the two benchmarks and present the results of a numerical simulation
of modest size.


title: Classical U(1) Lattice Gauge Theory in D=2

abstract:
  Under the hypothesis of no topological structure below a certain scale, we
prove that any U(1) lattice configuration corresponds to a classical U(1) gauge
field with zero local field strength; i.e. any local representative of the
pullback connection one-form is a pure gauge and the local curvature two-form
is thus identical zero. The topological information is completely carried by
the chart transitions. To each such U(1) lattice configuration we assign a
Chern number, which generally depends on the reconstruction of the bundle and
is only unique under certain restrictions.


title: Confinement and Topological Charge in the Abelian Gauge of QCD

abstract:
  We study the relation between instantons and monopoles in the abelian gauge.
First, we investigate the monopole in the multi-instanton solution in the
continuum Yang-Mills theory using the Polyakov gauge. At a large instanton
density, the monopole trajectory becomes highly complicated, which can be
regarded as a signal of monopole condensation. Second, we study instantons and
monopoles in the SU(2) lattice gauge theory both in the maximally abelian (MA)
gauge and in the Polyakov gauge. Using the $16^3 \times 4$ lattice, we find
monopole dominance for instantons in the confinement phase even at finite
temperatures. A linear-type correlation is found between the total
monopole-loop length and the integral of the absolute value of the topological
density (the total number of instantons and anti-instantons) in the MA gauge.
We conjecture that instantons enhance the monopole-loop length and promote
monopole condensation.


title: Thermodynamics of 1-flavor QCD

abstract:
  We present first results, for heavy to moderate quark masses, of a study of
thermodynamic properties of 1-flavor QCD, using the multiboson algorithm.


title: Non-perturbative O(a) improvement of lattice QCD

abstract:
  The coefficients multiplying the counterterms required for O($a$) improvement
of the action and the isovector axial current in lattice QCD are computed
non-perturbatively, in the quenched approximation and for bare gauge couplings
$g_0$ in the range $0 \leq g_0 \leq 1$. A finite-size method based on the
Schr\"odinger functional is employed, which enables us to perform all
calculations at zero or nearly zero quark mass. As a by-product the critical
hopping parameter $\kappa_c$ is obtained at all couplings considered.


title: Improving flavor symmetry in the Kogut-Susskind hadron spectrum

abstract:
  We study the effect of modifying the coupling of Kogut-Susskind quarks to the
gauge field by replacing the link matrix in the quark action by a "fat link",
or sum of link plus three-link paths. Flavor symmetry breaking, determined by
the mass difference between the Goldstone and non-Goldstone local pions, is
reduced by approximately a factor of two by this modification.


title: A Possible Lattice Chiral Gauge Theory

abstract:
  We analyze the dynamics of an $SU_L(2)\otimes U_R(1)$ chiral gauge theory on
a lattice with a large multifermion coupling $1\ll g_2 < \infty$. It is shown
that no spontaneous symmetry breaking occurs; the ``spectator'' fermion
$\psi_R(x)$ is a free mode; doublers are decoupled as massive Dirac fermions
consistently with the chiral gauge symmetry. Whether right-handed three-fermion
states disappear and chiral fermions emerge in the low-energy limit are
discussed. Provided right-handed three-fermion states disappear, we discuss the
chiral gauge coupling, Ward identities, the gauge anomaly and anomalous
$U_L(1)$ global current within the gauge-invariant prescription of
renormalization of the gauge perturbation theory.


title: Non-perturbative renormalization in lattice QCD

abstract:
  In this talk I will discuss a number of approaches designed to deal with the
problem of setting up a fully non-perturbative renormalization procedure in
lattice QCD. Methods based on Ward-Takahashi identities on hadronic states, on
imposing chiral selection rules on amplitudes with external quark/gluon legs,
on the use of the Schr\"{o}dinger functional and on ``heating and cooling''
Monte Carlo steps are reviewed. I conclude with some remarks on the possibility
of defining next order terms (higher twists, ``condensates", ...) in short
distance expansions.


title: The Drell-Yan process and Deep Inelastic Scattering from the lattice

abstract:
  We report on measurements of the h_1 structure function, relevant to
calculating cross-sections for the Drell-Yan process. This is a quantity which
can not be measured in Deep Inelastic Scattering, it gives additional
information on the spin carried by the valence quarks, as well as insights on
how relativistic the quarks are.


title: Probing the interior of the Colour Flux Tube

abstract:
  In the dual superconductivity description of quark confinement the core of
the flux tube connecting a quark pair belongs to a deconfined, hot phase. This
can be checked in numerical experiments on 3D $Z_2$ gauge model. It is also
pointed out that the Svetitsky-Yaffe conjecture provides analytic expressions
for the distribution of the flux density around quark sources at critical
temperature.


title: String Effects in the Wilson Loop: a high precision numerical test

abstract:
  We test numerically the effective string description of the infrared limit of
lattice gauge theories in the confining regime. We consider the 3d Z(2) lattice
gauge theory, and we define ratios of Wilson loops such that the predictions of
the effective string theory do not contain any adjustable parameters. In this
way we are able to obtain a degree of accuracy high enough to show
unambiguously that the flux--tube fluctuations are described, in the infrared
limit, by an effective bosonic string theory.


title: Quantum Link Models: A Discrete Approach to Gauge Theories

abstract:
  We construct lattice gauge theories in which the elements of the link
matrices are represented by non-commuting operators acting in a Hilbert space.
These quantum link models are related to ordinary lattice gauge theories in the
same way as quantum spin models are related to ordinary classical spin systems.
Here U(1) and SU(2) quantum link models are constructed explicitly. As
Hamiltonian theories quantum link models are nonrelativistic gauge theories
with potential applications in condensed matter physics. When formulated with a
fifth Euclidean dimension, universality arguments suggest that dimensional
reduction to four dimensions occurs. Hence, quantum link models are also
reformulations of ordinary quantum field theories and are applicable to
particle physics, for example to QCD. The configuration space of quantum link
models is discrete and hence their numerical treatment should be simpler than
that of ordinary lattice gauge theories with a continuous configuration space.


title: Instanton, Monopole and Confinement

abstract:
  We study the correlation between instantons and QCD-monopoles both in the
lattice gauge theory and in the multi-instanton system using the maximally
abelian gauge. First, we find the existence of an almost linear correlation
between the total length of monopole trajectories and the total number of
pseudoparticles (instantons and anti-instantons) in the $16^{3}\times4$ SU(2)
lattice. Second, we study the features of QCD-monopole in the SU(2)
multi-instanton vacuum on the $16^{4}$ lattice as a random ensemble of
pseudoparticles. A signal of monopole condensation is found as the clustering
of monopole trajectories, when the topological pseudoparticles is sufficiently
dense.


title: Softening Transitions with Quenched 2D Gravity

abstract:
  We perform extensive Monte Carlo simulations of the 10-state Potts model on
quenched two-dimensional $\Phi^3$ gravity graphs to study the effect of
quenched connectivity disorder on the phase transition, which is strongly first
order on regular lattices. The numerical data provides strong evidence that,
due to the quenched randomness, the discontinuous first-order phase transition
of the pure model is softened to a continuous transition.


title: Logarithmic Corrections in the 2D XY Model

abstract:
  Using two sets of high-precision Monte Carlo data for the two-dimensional XY
model in the Villain formulation on square $L \times L$ lattices, the scaling
behavior of the susceptibility $\chi$ and correlation length $\xi$ at the
Kosterlitz-Thouless phase transition is analyzed with emphasis on
multiplicative logarithmic corrections $(ln L)^{-2r}$ in the finite-size
scaling region and $(ln \xi)^{-2r}$ in the high-temperature phase near
criticality, respectively. By analyzing the susceptibility at criticality on
lattices of size up to $512^2$ we obtain $r = -0.0270(10)$, in agreement with
recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang
zeros in the cosine formulation of the XY model. By studying susceptibilities
and correlation lengths up to $\xi \approx 140$ in the high-temperature phase,
however, we arrive at quite a different estimate of $r = 0.0560(17)$, which is
in good agreement with recent analyses of thermodynamic Monte Carlo data and
high-temperature series expansions of the cosine formulation.


title: Light Quark Masses and the CP violation parameter $\epsilon'/\epsilon$

abstract:
  We present estimates of light quarks masses using lattice data. Our main
results are based on a global analysis of all the published data for Wilson and
Staggered fermions, both in the quenched approximation and with $n_f=2$
dynamical flavors. The Wilson and Staggered results agree after extrapolation
to the continuum limit for both the $n_f=0,2$ theories. Our best estimates, in
the MSbar scheme at scale $2 GeV$, are $mbar=3.2(4) MeV$ and $m_s = 90(20) MeV$
in the quenched approximation, and $mbar ~ 2.7 MeV$ and $m_s ~ 70 MeV$ for the
$n_f=2$ theory. These estimates are significantly smaller than phenomenological
estimates based on sum rules, but maintain the ratios predicted by chiral
perturbation theory. Along with the new estimates of 4-fermion operators, lower
quark masses have a significant impact on the extraction of
$\epsilon'/\epsilon$ from the Standard Model.


title:
Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to
  Estimate Correlation Lengths

abstract:
  We report numerical simulations of two-dimensional $q$-state Potts models
with emphasis on a new quantity for the computation of spatial correlation
lengths. This quantity is the cluster-diameter distribution function
$G_{diam}(x)$, which measures the distribution of the diameter of
stochastically defined cluster. Theoretically it is predicted to fall off
exponentially for large diameter $x$, $G_{diam} \propto \exp(-x/\xi)$, where
$\xi$ is the correlation length as usually defined through the large-distance
behavior of two-point correlation functions. The results of our extensive Monte
Carlo study in the disordered phase of the models with $q=10$, 15, and $20$ on
large square lattices of size $300 \times 300$, $120 \times 120$, and $80
\times 80$, respectively, clearly confirm the theoretically predicted behavior.
Moreover, using this observable we are able to verify an exact formula for the
correlation length $\xi_d(\beta_t)$ in the disordered phase at the first-order
transition point $\beta_t$ with an accuracy of about $1%-2%$ for all considered
values of $q$. This is a considerable improvement over estimates derived from
the large-distance behavior of standard (projected) two-point correlation
functions, which are also discussed for comparison.


title: $B$ and $B_c$ mesons with NRQCD and Clover actions

abstract:
  We present preliminary results from our study of the heavy-light spectrum and
decay constants. For the heavy quark, we use NRQCD at various masses around and
above the $b$ quark mass. For the first time, the heavy quark action and the
heavy-light current consistently include corrections at second order in the
non-relativistic expansion, as well as the leading finite $a$ corrections. The
light quarks are simulated using a tadpole-improved Clover action at various
masses in the strange and $c$ quark region.


title:
Continuum Behaviour of Lattice QED, Discretized with One-Sided Lattice
  Differences, in One-Loop Order

abstract:
  A lattice action for QED is considered, where the derivatives in the Dirac
operator are replaced by one-sided lattice differences. A systematic expansion
in the lattice spacing of the one-loop contribution to the fermion self energy,
vacuum polarization tensor and vertex function is carried out for an arbitrary
choice of one-sided lattice differences. It is shown that only the vacuum
polarization tensor possesses the correct continuum limit, while the fermion
self energy and vertex function receive non-covariant contributions. A lattice
action, discretized with a fixed choice of one-sided lattice differences
therefore does not define a renormalizable field theory. The non-covariant
contributions can however be eliminated by averaging the expressions over all
possible choices of one-sided lattice differences.


title:
Asymmetry Parameter Role in Description of Phase Structure of Lattice
  Gluodynamics at Finite Temperature

abstract:
  The role of lattice asymmetry parameter in description of the SU(2)
gluodynamics phase structure at finite temperature is studied analytically. The
fact that renormalization group relations which permit to remove the lattice
asymmetry parameter from the thermodynamical quantities in the "naive" limit
don't do the same in the approximation SU(N) = Z(N) keeping the "naive" limit
results at the same time was point out. An additional condition which would fix
asymmetry parameter is needed for this dependence removal.


title: Distribution of Instanton and Monopole Clustering

abstract:
  We study the relation between the instanton distribution and the monopole
loop length in the SU(2) gauge theory with the abelian gauge fixing. We measure
the monopole current from the multi-instanton ensemble on the $16^4$ lattice
using the maximally abelian gauge. When the instanton density is dilute, there
appear only small monopole loops. On the other hand, in the dense case, there
appears one very long monopole loop, which is responsible for the confinement
property, in each gauge configuration. We find a clear monopole clustering in
the histogram of the monopole loop length from 240 gauge configurations.


title:
Topological charge on the lattice: a field theoretical view of the
  geometrical approach

abstract:
  We construct sequences of ``field theoretical'' (analytical) lattice
topological charge density operators which formally approach geometrical
definitions in 2-d $CP^{N-1}$ models and 4-d $SU(N)$ Yang Mills theories. The
analysis of these sequences of operators suggests a new way of looking at the
geometrical method, showing that geometrical charges can be interpreted as
limits of sequences of field theoretical (analytical) operators. In
perturbation theory renormalization effects formally tend to vanish along such
sequences. But, since the perturbative expansion is asymptotic, this does not
necessarily lead to well behaved geometrical limits. It indeed leaves open the
possibility that non-perturbative renormalizations survive.


title: Center Dominance and Z2 Vortices in SU(2) Lattice Gauge Theory

abstract:
  We find, in close analogy to abelian dominance in maximal abelian gauge, the
phenomenon of center dominance in maximal center gauge for $SU(2)$ lattice
gauge theory. Maximal center gauge is a gauge-fixing condition that preserves a
residual $Z_2$ gauge symmetry; ``center projection'' is the projection of
$SU(2)$ link variables onto $Z_2$ center elements, and ``center dominance'' is
the fact that the center-projected link elements carry most of the information
about the string tension of the full theory. We present numerical evidence that
the thin $Z_2$ vortices of the projected configurations are associated with
``thick'' $Z_2$ vortices in the unprojected configurations. The evidence also
suggests that the thick $Z_2$ vortices may play a significant role in the
confinement process.


title: Simulations with Complex Measure

abstract:
  A method is proposed to handle the sign problem in the simulation of systems
having indefinite or complex-valued measures. In general, this new approach,
which is based on renormalisation blocking, is shown to yield statistical
errors smaller than the crude Monte Carlo method using absolute values of the
original measures. The improved method is applied to the 2D Ising model with
temperature generalised to take on complex values. It is also adapted to
implement Monte Carlo Renormalisation Group calculations of the magnetic and
thermal critical exponents.


title:
Effective Constraint Potential for Abelian Monopole in SU(2) Lattice
  Gauge Theory

abstract:
  We describe numerical calculation results for the probability distribution of
the value of the monopole creation operator in the SU(2) lattice gluodynamics.
We work in the maximal abelian projection. It occurs that at low temperatures,
below the deconfinement phase transition, the maximum of the distribution is
shifted from zero, which means that the effective constraint potential is of
the Higgs type. Above the phase transition the minimum of the potential (the
maximum of the monopole field distribution) is at the zero value of the
monopole field. This fact confirms the existence of the abelian monopole
condensate in the confinement phase of lattice gluodynamics, and agrees with
the dual superconductor model of the confining vacuum.


title: A Wilson-Majorana Regularization for Lattice Chiral Gauge Theories

abstract:
  We discuss the regularization of chiral gauge theories on the lattice
introducing only physical degrees of freedom. This is obtained by writing the
Wilson term in a Majorana form, at the expense of the U(1) symmetry related to
fermion number conservation. The idea of restoring chiral invariance in the
continuum by introducing a properly chosen set of counterterms to be added to
the tree level action is checked against one-loop perturbative calculations.


title: New results on topological susceptibility in SU(3) gauge theory

abstract:
  We survey recent lattice results on QCD topological properties. The behaviour
of the topological susceptibility at the deconfining phase transition has been
determined. This advance has been made possible by an i) an improvement of the
topological charge operator and ii) a non-perturbative determination of
renormalizations.


title: Heavy Light Weak Matrix Elements

abstract:
  I review the status of lattice calculations of heavy-light weak matrix
elements, concentrating on semileptonic B decays to light mesons, B -> K*
gamma, the B meson decay constant, f_B, and the mixing parameter B_B.


title: The Structure of Flux-tubes in SU(2)

abstract:
  The spatial distribution of the action and energy in the colour fields of
flux-tubes is studied in lattice SU(2) field theory for static quarks at
separations up to 1 fm. Special attention is paid to the structure of the
colour fields associated with an excited flux-tube with E_u symmetry. We
compare our results with hadronic string and flux-tube models. Sum rules are
used to extract generalised beta-functions, to describe the expected colour
field behaviour and to cross check the methods used.


title: Hubbard Model and Luscher fermions

abstract:
  We discuss numerical complexity of the L\"uscher algorithm applied to the
Hubbard Model. In particular we present comparison to a certain algorithm based
on direct computation of the fermionic determinant.


title: Curing O(a) Errors in 3-D Lattice SU(2) x U(1) Higgs Theory

abstract:
  We show how to make O(a) corrections in the bare parameters of 3-D lattice
SU(2) times U(1) Higgs theory which remove O(a) errors in the match between the
infrared behavior and the infrared behavior of the continuum theory. The
corrections substantially improve the convergence of lattice data to a small a
limit.


title: Lattice Monte Carlo Data versus Perturbation Theory

abstract:
  Differences between lattice Monte Carlo data and perturbation theory (for
example the lack of asymptotic scaling) are usually associated with the `bad'
behaviour of the bare lattice coupling g_0 due to the effects of large (and
unknown) higher order terms in g_0. In this philosophy a new, renormalised
coupling g' is defined with the aim of making the higher order coefficients of
the perturbative series in g' as small as possible.
  In this paper an alternative scenario is discussed where lattice artifacts
are proposed as the cause of the disagreement between Monte Carlo data and the
g_0-perturbative series. We find that with the addition of a lattice artifact
term, the usual asymptotic scaling expression in g_0 is in excellent agreement
with Monte Carlo data. Lattice data studied includes the string tension, the
hadronic scale r_0, the discrete beta function, M_rho, f_pi and the 1P-1S
splitting in charmonium.


title: Comparing Different Improvement Programs for the N-Vector Model

abstract:
  We discuss the connection between various types of improved actions in the
context of the two-dimensional sigma-model. We also discuss spectrum-improved
actions showing that these actions do not have any improved behaviour. An
O(a^2) on-shell improved action with all couplings defined on a plaquette and
satisfying reflection positivity is also explicitly constructed.


abstract:
  The differences between lattice Monte Carlo data and perturbation theory are
usually associated with the ``bad'' behaviour of the bare lattice coupling g_0
due to the effects of large (and unknown) higher order coefficients in the g_0
perturbative series. In this philosophy a new, renormalised coupling g' is
defined with the aim of reducing the higher order coefficients of the
perturbative series in g'. An improvement in the agreement between lattice data
and this new perturbation series is generally observed.
  In this paper an alternative scenario is discussed where lattice artifacts
are proposed as the cause of the disagreement between lattice data and the
g_0-perturbative series. We find that this interpretation provides excellent
agreement between lattice data and perturbation theory in g_0 corrected for
lattice artifacts. We show that this viewpoint leads typically to an order of
magnitude improvement in the agreement between lattice data and perturbation
theory, compared to typical g' perturbation expansions. The success of this
procedure leads to a determination of Lambda_MSbar^{N_f=0} of 220 +- 20 MeV.
Lattice data studied includes quenched values of the string tension, the
hadronic scale r_0, the discrete beta function Delta\beta, M_rho, f_pi and the
1P-1S splitting in charmonium. The new 3-loop term of the lattice beta-
function has been incorporated in this study.
  A discussion of the implication of this result for lattice calculations is
presented.


title: A new algorithm for numerical simulation of Langevin equations

abstract:
  Formulated is a new systematic method for obtaining higher order corrections
in numerical simulation of stochastic differential equations (SDEs), i.e.,
Langevin equations. Random walk step algorithms within a given order of finite
$\Delta t$, are obtained so as to reproduce within that order a corresponding
transition density of the Fokker-Planck equations, in the weak Taylor
approximation scheme. A great advantage of our method is its
straightforwardness such that direct perturbative calculations produce the
algorithm as an end result, so that the procedure is tractable by computer.
Examples in general form for curved space cases as well as flat space cases are
given in some order of approximations. Simulations are performed for specific
examples of U(1) system and SU(2) systems, respectively.


title: The PZ method for estimating determinant ratios, with applications

abstract:
  We introduce a new method for estimating determinants or determinant ratios
of large matrices, which combines the techniques of Pad\`{e} approximation with
rational functions and $Z_{2}$ noise estimation of traces of large matrices.
The method requires simultaneously solving several matrix equations, which can
be conveniently accomplished using the MR method. We include some preliinary
results, and indicate potential applications to non-Hermitian matrices, and
Hybrid Monte Carlo without pseudofermions.


title:
The Pseudo Specific Heat in SU(2) Gauge Theory : Finite Size Dependence
  and Finite Temperature Effects

abstract:
  We investigate the pseudo specific heat of SU(2) gauge theory near the
crossover point on $4^4$ to $16^4$ lattices. Several different methods are used
to determine the specific heat. The curious finite size dependence of the peak
maximum is explained from the interplay of the crossover phenomenon with the
deconfinement transition occurring due to the finite extension of the lattice.
We find, that for lattices of size $8^4$ and larger the crossover peak is
independent of lattice size at $\beta_{co}=2.23(2)$ and has a peak height of
$C_{V,co}=1.685(10)$. We conclude therefore that the crossover peak is not the
result of an ordinary phase transition. Further, the contributions to $C_V$
from different plaquette correlations are calculated. We find, that at the peak
and far outside the peak the ratio of contributions from orthogonal and
parallel plaquette correlations is different. To estimate the finite
temperature influence on symmetric lattices far off the deconfinement
transition point we calculate the modulus of the lattice average of the
Polyakov loop on these lattices and compare it to predictions from a random
walk model.


title: Hybrid Monte Carlo Without Pseudofermions

abstract:
  We introduce a dynamical fermion algorithm which is based on the hybrid Monte
Carlo (HMC) algorithm, but without pseudofermions. The molecular dynamics steps
in HMC are retained except the derivatives with respect to the gauge fields are
calculated with the $Z_2$ noise. The determinant ratios are estimated with the
Pa\`{d}e - $Z_2$ method. Finally, we use the Kennedy-Kuti linear accept/reject
method for the Monte Carlo step which is shown to respect detailed balance. We
comment on the comparison of this algorithm with the pseudofermion algorithm.


title:
Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$
  Principal Chiral Model

abstract:
  We carry out a high-precision simulation of the two-dimensional $SU(3)$
principal chiral model at correlation lengths $\xi$ up to $\sim 4 \times 10^5$,
using a multi-grid Monte Carlo (MGMC) algorithm and approximately one year of
Cray C-90 CPU time. We extrapolate the finite-volume Monte Carlo data to
infinite volume using finite-size-scaling theory, and we discuss carefully the
systematic and statistical errors in this extrapolation. We then compare the
extrapolated data to the renormalization-group predictions. The deviation from
asymptotic scaling, which is $\approx 12%$ at $\xi \sim 25$, decreases to
$\approx 2%$ at $\xi \sim 4 \times 10^5$. We also analyze the dynamic critical
behavior of the MGMC algorithm using lattices up to $256 \times 256$, finding
the dynamic critical exponent $z_{int,{\cal M}^2} \approx 0.45 \pm 0.02$
(subjective 68% confidence interval). Thus, for this asymptotically free model,
critical slowing-down is greatly reduced compared to local algorithms, but not
completely eliminated.


title:
Stability of the Bulk Phase Diagram of the SU(2) Lattice Gauge Theory
  with Fundamental - Adjoint Action

abstract:
  Using improved mean field and strong coupling expansions we re-analyse the
bulk phase diagram of the fundamental-adjoint action of the SU(2) Lattice Gauge
Theory. We find that the qualitative features of the bulk phase diagram are
robust and unchanged by the inclusion of higher order terms. On the other hand,
some of the quantitative features, such as the location of the endpoint of the
line of bulk phase transitions, seem to be strongly dependent on the higher
terms of the strong coupling expansion.


title:
Scaling in SU(3) Pure Gauge Theory with a Renormalization Group Improved
  Action

abstract:
  We study the scaling properties of the static quark potential and the ratio
of the critical temperature $T_c$ to the square root of the string tension
$\sigma$ in the SU(3) pure gauge theory using a renormalization group improved
action. We first determine the critical coupling $\beta_c$ on lattices with
temporal extension $N_t=3$, 4, and 6, and then calculate the static quark
potential at the critical couplings on lattices at zero temperature. We note
that the static quark potentials obtained are rotationally invariant with
errors of at most 1 - 2 % in all the three cases, and that the potential $V(R)$
in physical units scales in the whole region of $R$ investigated. The values of
$T_{c}/\sqrt{\sigma}$ for the three cases in the infinite volume limit are
identical within errors. We estimate the value in the continuum limit to be
$T_{c}/\sqrt{\sigma} = 0.656(4)$, which is slightly larger than the value in
the continuum limit from the one-plaquette action, 0.629(3).


title: $B - \bar B$ Mixing in the HQET

abstract:
  We present a high statistics, quenched lattice calculation of the
B-parameters $B_{B_d}$ and $B_{B_s}$, computed at lowest order in the HQET. The
results were obtained using a sample of 600 quenched gauge field
configurations, generated by Monte Carlo simulation at $\beta=6.0$ on a
$24^{3}\times 40$ lattice. For the light quarks the SW-Clover action was used;
the propagator of the lattice HQET was also tree-level improved. Our best
estimate of the renormalization scale independent B-parameter is $\hat{B}_{B_d}
= 1.03 \pm 0.06 \pm 0.18$. $\hat{B}_{B_d}$ has been obtained by using
``boosted'' perturbation theory to calculate the renormalization constants
which relate the matrix elements of the lattice operators to the corresponding
amplitudes in the continuum. Due to the large statistics, the errors in the
extraction of the matrix elements of the relevant bare operators are rather
small. The main systematic error, corresponding to $\pm 0.18$ in the above
result, comes from the uncertainty in the evaluation of the renormalization
constants, for which the one-loop corrections are rather large. The
non-perturbative evaluation of these constants will help to reduce the final
error. We also obtain $\hat{B}_{B_s}/\hat{B}_{B_d} = 1.01 \pm 0.01$ and
$f^2_{B_s}\hat{B}_{B_s}/f^2_{B_d}\hat{B}_{B_d} = 1.38 \pm 0.07$.


title:
Relating U(1) monopole configurations to SU(2) saddle-point
  configurations

abstract:
  We have studied field configurations of the 3-dimensional Georgi-Glashow
model which interpolate between the $U(1)$ and the $SU(2)$ limits. In the
intermediate region, these configurations contain 't-Hooft--Polyakov monopoles.
We use cooling and extremization to find these configurations and investigate
their evolution as we adiabatically move towards the $U(1)$ and the $SU(2)$
limits. We also evolve an $SU(2)$ saddle point solution towards the $U(1)$
limit to see the relation between the unstable solutions in the $SU(2)$ theory
and the stable ones in the $U(1)$ theory.


title: A calculation of the $B_{B}$ parameter in the static limit

abstract:
  We calculate the $B_{B}$ parameter, relevant for $\overline{B}^0$ -- $B^0$
mixing, from a lattice gauge theory simulation at $\beta = 6.0$. The bottom
quarks are simulated in the static theory, the light quarks with Wilson
fermions. Improved smearing functions produced by a variational technique,
MOST, are used to reduce statistical errors and minimize excited-state
contamination of the ground-state signal. We obtain $B_B(4.33 GeV) =
0.98^{+4}_{-4}$ (statistical) $^{+3}_{-18}$ (systematic) which corresponds to
$\widehat{B}_B = 1.40^{+6}_{-6}$ (statistical) $^{+4}_{-26}$ (systematic) for
the one-loop renormalization-scheme-independent parameter. The systematic
errors include the uncertainty due to alternative (less favored) treatments of
the perturbatively-calculated mixing coefficients; this uncertainty is at least
as large as residual differences between Wilson-static and clover-static
results. Our result agrees with extrapolations of results from relativistic
(Wilson) heavy quark simulations.


title:
Light vector meson decay constants and the renormalization factor from a
  tadpole-improved action

abstract:
  The rho, K* and phi decay constants and the vector current renormalization
factor are studied by using an O(a^2) classically-improved, tadpole-improved
action. Tree-level calculations are used to show how the classical improvement
of the action, involving next-nearest-neighbour timesteps, is transferred to
the matrix elements. Simulations are performed on coarse lattices and compared
to Wilson results from both coarse and fine lattices. The improved action data
are found to resemble Wilson data obtained at 1/3 of the lattice spacing, which
is the same degree of improvement that is seen by comparing the mass spectra.


title:
Unstable Modes and Confinement in the Lattice Schr\"odinger Functional
  Approach

abstract:
  We analyze the problem of the Nielsen-Olesen unstable modes in the SU(2)
lattice gauge theory by means of a recently introduced gauge-invariant
effective action. We perform numerical simulations in the case of a constant
Abelian chromomagnetic field. We find that for lattice sizes above a certain
critical length the density of effective action shows a behaviour compatible
with the presence of the unstable modes. We put out a possible relation between
the dynamics of the unstable modes and the confinement.


title: The perfect action for non-degenerate staggered fermions

abstract:
  The perfect action of free staggered fermions is calculated by blocking from
the continuum for degenerate and non-degenerate flavor masses. The symmetry
structure, connecting flavor transformations and translations, is explained
directly from the blocking scheme. It is convenient to use a modified Fourier
transformation, respecting this connection, to treat the spin-flavor structure
of the blockspins. The perfect action remains local in the non-degenerate case;
it is explicitly calculated in two dimensions. I finally comment on the
relation of the blocking scheme to the transition from Dirac-K\"ahler fermions
to staggered fermions.


title: The Anti-Ferromagnetic Vacuum

abstract:
  Certain effective vertices may generate a non-homogeneous, periodic vacuum
structure. The excitations above such a vacuum are studied in the framework of
the $\phi^4$ and gauge models. The formation of the non-homogeneous vacuum is
accompanied by the dynamical breakdown of the space-time inversion symmetry.
Chiral transformation is introduced for bosons in close analogy with lattice
fermions.


title: U(1) Lattice Gauge theory and its Dual

abstract:
  The three dimensional U(1) Lattice Gauge, in the weak coupling limit, is dual
to a Discrete Gaussian model. We investigate this dual model and use it to
calculate properties of the U(1) theory. We find that, because of the nature of
the dual model, its advantages are outweighed by large autocorrelation times
generated when the dual system becomes disordered.


title:
Monte Carlo study of very weak first-order transitions in the
  three-dimensional Ashkin-Teller model

abstract:
  We propose numerical simulations of the Ashkin-Teller model as a foil for
theoretical techniques for studying very weakly first-order phase transitions
in three dimensions. The Ashkin-Teller model is a simple two-spin model whose
parameters can be adjusted so that it has an arbitrarily weakly first-order
phase transition. In this limit, there are quantities characterizing the
first-order transition which are universal: we measure the relative
discontinuity of the specific heat, the correlation length, and the
susceptibility across the transition by Monte Carlo simulation.


title: Chiral zero modes on the domain-wall model in 4+1 dimensions

abstract:
  We investigate an original domain-wall model in 4+1 dimensions numerically in
the presence of U(1) dynamical gauge field only in an extra dimension,
corresponding to a weak coupling limit of 4-dimensional physical gauge
coupling. Using a quenched approximation we carry out numerical simulation for
this model at $\beta_{s} (= 1 / g^{2}_{s}) =$ 0.29 (``symmetric'' phase) and
0.5 (``broken'' phase), where $g_s$ is the gauge coupling constant of the extra
dimension. In the broken phase, we found that there exists a critical value of
a domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero
mode on the domain wall from the one without it in the same case of
(2+1)-dimensional model. On the other hand, in the symmetric phase, our
numerical data suggest that the chiral zero modes disappear in the infinite
limit of 4-dimensional volume. From these results it seems difficult to
construct the U(1) lattice chiral gauge theory via an original domain-wall
formulation.


title:
Domain walls, $Z(N)$ charge and $A_0$ condensate: a canonical ensemble
  study

abstract:
  The deconfinement phase transition is studied in the ensemble canonical with
respect to triality. Since this ensemble implies a projection to the zero
triality sector of the theory we introduce a quantity which is insensitive to
$Z(N_c)$ symmetry but can reveal a critical behaviour in the theory with
dynamical quarks. Further, we argue that in the canonical ensemble description
of full QCD there exist domains of different $Z(N_c)$ phases which are
degenerate and possess normal physical properties. This contradicts the
predictions of the grand canonical ensemble. We propose a new order parameter
to test the realization of the discrete $Z(N_c)$ symmetry at finite temperature
and calculate it for the case of $Z(2)$ gauge fields coupled to fundamental
fermions.


title: Another Look at Neural Multigrid

abstract:
  We present a new multigrid method called neural multigrid which is based on
joining multigrid ideas with concepts from neural nets. The main idea is to use
the Greenbaum criterion as a cost functional for the neural net. The algorithm
is able to learn efficient interpolation operators in the case of the ordered
Laplace equation with only a very small critical slowing down and with a
surprisingly small amount of work comparable to that of a Conjugate Gradient
solver. In the case of the two-dimensional Laplace equation with SU(2) gauge
fields at beta=0 the learning exhibits critical slowing down with an exponent
of about z = 0.4. The algorithm is able to find quite good interpolation
operators in this case as well. Thereby it is proven that a practical true
multigrid algorithm exists even for a gauge theory. An improved algorithm using
dynamical blocks that will hopefully overcome the critical slowing down
completely is sketched.


title: One-loop anisotropy for improved actions

abstract:
  We determine the one-loop correction to the anisotropy factor for the square
Symanzik improved lattice action, extracted fromthe finite volume effective
action for SU(N) gauge theories in the background of a zero-momentum gauge
field. The result is smaller by approximately a factor 3 than the one-loop
correction for the anisotropic Wilson action. We also comment on the
Hamiltonian limit.


title: The Renormalization Group and Dynamical Triangulations

abstract:
  A block spin renormalization group approach is introduced which can be
applied to dynamical triangulations in any dimension.


title:
Continuum limit of finite temperature $\lambda\phi^4_3$ from lattice
  Monte Carlo

abstract:
  The $\phi^4_3$ model at finite temperature is simulated on the lattice. For
fixed $N_t$ we compute the transition line for $N_s \to \infty$ by means of
Finite Size Scaling techniques. The crossings of a Renormalization Group
trajectory with the transition lines of increasing $N_t$ give a well defined
limit for the critical temperature in the continuum. By considering different
RG trajectories, we compute $T^c/g$ as a function of the renormalized
parameters.


title: Finite Temperature Properties of the SO(3) Lattice Gauge Theory

abstract:
  We make a numerical study of the finite temperature properties of the SO(3)
lattice gauge theory. As its symmetry properties are quite different from those
of the SU(2) LGT, a different set of observables have to be considered in this
model. We study several observables, such as, the plaquette square, the Z(2)
monopole density, the fundamental and adjoint Wilson line, and the tiled Wilson
line correlation function. Our simulations show that the Z(2) monopoles
condense at strong coupling just as in the bulk system. This transition is seen
at approximately the same location as in the bulk system. A surprising
observation is the multiple valuedness of the adjoint Wilson line at high
temperatures. At high temperatures, we observe long lived metastable states in
which the adjoint Wilson line takes positive and negative values. The numerical
values of other observables in these two states appear to be almost the same.
We study these states using different methods and also make comparisons with
the high temperature behaviour of the SU(2) LGT. Finally, we discuss various
interpretations of our results and point out their relevance for the phase
diagram of the SO(3) LGT at finite temperature.


title: The Abelianicity of Cooled SU(2) Lattice Configurations

abstract:
  We introduce a gauge-invariant measure of the local "abelianicity" of any
given lattice configuration in non-abelian lattice gauge theory; it is
essentially a comparison of the magnitude of field strength commutators to the
magnitude of the field strength itself. This measure, in conjunction with the
cooling technique, is used to probe the SU(2) lattice vacuum for a possible
large-scale abelian background, underlying the local short-range field
fluctuations. We do, in fact, find a substantial rise in abelianicity over 10
cooling steps or so, after which the abelianicity tends to drop again.


title: Is trivial the antiferromagnetic RP(2) model in four dimensions?

abstract:
  We study the antiferromagnetic RP(2) model in four dimensions. We find a
second order transition with two order parameters, one ferromagnetic and the
other antiferromagnetic. The antiferromagnetic sector has mean-field critical
exponents and a renormalized coupling which goes to zero in the continuum
limit. The exponents of the ferromagnetic channel are not the mean-field ones,
but the difference can be interpreted as logarithmic corrections. We perform a
detailed analysis of these corrections and conclude the triviality of the
continuum limit of this model.


title: The critical points of lattice QCD with a non--zero quark density

abstract:
  We study the interplay of quark number density and chiral symmetry in lattice
QCD. We suggest that both are controlled by the eigenvalue spectrum of the
fermionic propagator matrix, which shapes the pattern of zeros of the partition
function. The onset of the quark current would be triggered by the lowest lying
eigenvalue, the chiral transition by the density of zeros, the two critical
points being distinct in full QCD, and coincident in the quenched
approximation. Our preliminary estimate for the critical point in full QCD in
the infinite couling limit compares favourably with the predictions of the
strong coupling expansions and of numerical simulations based on exact,
alternative representations of the partition function. Several reasons of
perplexity however remain, which are briefly discussed.


title:
The exact equivalence of the one-flavour lattice Thirring model with
  Wilson fermions to a two-colour loop model

abstract:
  Within Euclidean lattice field theory an exact equivalence between the
one-flavour 2D Thirring model with Wilson fermions and Wilson parameter $r = 1$
to a two-colour loop model on the square lattice is established. For
non-interacting fermions this model reduces to an exactly solved loop model
which is known to be a free fermion model. The two-colour loop model equivalent
to the Thirring model can also be understood as a 4-state 49-vertex model.


title: A determination of the mass gap in the O(n) sigma model

abstract:
  We calculate the finite volume mass gap $M(L)$ at 3-loop level in the
non-linear O($n$) $\sigma$-model in two dimensions in small volumes. By
applying the Monte Carlo measurements of the running coupling $\bar
g^2(L)=2nM(L)L/(n-1)$ by L\"uscher, Weisz and Wolff measured in units of the
physical mass gap $m$, the result is used to determine $m$ in units of the
$\Lambda$-parameter in the O(3) and O(4) models. Our determinations show good
agreement with those by Hasenfratz, Maggiore and Niedermayer in both models. We
note that this manuscript has been revised in our paper hep-lat/9810025 by
using the corrected four-loop $\beta$-function on the lattice.


title: Weak Matrix Elements on the Lattice: Recent Developments in K-Physics

abstract:
  Some recent developments in the calculation of weak matrix elements on the
lattice are reviewed. In particular, we concentrate on the application of MPSTV
non-perturbative renormalization method to the operators relevant to kaon
physics. The chiral behaviour of the $B_K$ parameter and the long-standing
question of the $\Delta I=1/2$ rule are discussed.


title: Yang-Lee zeros of a random matrix model for QCD at finite density

abstract:
  We study the Yang-Lee zeros of a random matrix partition function with the
global symmetries of the QCD partition function. We consider both zeros in the
complex chemical potential plane and in the complex mass plane. In both cases
we find that the zeros are located on a curve. In the thermodynamic limit, the
zeros appear to merge to form a cut. The shape of this limiting curve can be
obtained from a saddle-point analysis of the partition function. An explicit
solution for the line of zeros in the complex chemical potential plane at zero
mass is given in the form of a transcendental equation.


title: Comparison of Multi-quark Matrix Inversion Algorithms

abstract:
  We test iterative algorithms, MR, QMR$\gamma_5$ and BiCG$\gamma_5$, to
compare their efficiency in matrix inversion with multi-quarks (shifted
matrices) within one iteration process. Our results on the 8^3 x 12 and 16^3 x
24 show that MR admits multi-quark calculation with less memory requirement,
whereas QMR is faster for the single quark calculation.


title: Improving Lattice Quark Actions

abstract:
  We explore the first stage of the Symanzik improvement program for lattice
Dirac fermions, namely the construction of doubler-free, highly improved
classical actions on isotropic as well as anisotropic lattices (where the
temporal lattice spacing, a_t, is smaller than the spatial one). Using field
transformations to eliminate doublers, we derive the previously presented
isotropic D234 action with O(a^3) errors, as well as anisotropic D234 actions
with O(a^4) or O(a_t^3, a^4) errors. Besides allowing the simulation of heavy
quarks within a relativistic framework, anisotropic lattices alleviate
potential problems due to unphysical branches of the quark dispersion relation
(which are generic to improved actions), facilitate studies of lattice
thermodynamics, and allow accurate mass determinations for particles with bad
signal/noise properties, like glueballs and P-state mesons. We also show how
field transformations can be used to completely eliminate unphysical branches
of the dispersion relation. Finally, we briefly discuss future steps in the
improvement program.


title: Hybrid mesons from quenched QCD

abstract:
  We use lattice methods to evaluate from first principles the spectrum of
hybrid mesons produced by gluonic excitations in quenched QCD with quark masses
near the strange quark mass. For the spin-exotic mesons with $J^{PC}=1^{-+},\
0^{+-}$, and $2^{+-}$ which are not present in the quark model, we determine
the lightest state to be $1^{-+}$ with mass of 2.0(2) GeV.


title: The U(1) Problem in Chiral Random Matrix Models

abstract:
  We show that conventional asymmetric chiral random matrix models (ChRMM),
with a gaussian distribution in the asymmetry, provide for a screening of the
topological charge and a resolution of the $U(1)$ problem in the unquenched
approximation. Our exact results to order $1/N$ are in agreement with numerical
estimates using large ensembles of asymmetric ChRMM with gaussian
distributions.


title: Wilson--Yukawa Chiral Model on Lattice and Non-commutative Geometry

abstract:
  Based upon the mathematical formulas of Lattice gauge theory and
non-commutative geometry differential calculus, we developed an approach of
generalized gauge theory on a product of the spacetime lattice and the two
discrete points(or a $Z_2$ discrete group). We introduce a differentiation for
non-nearest-neighbour points and find that this differentiation may lead to the
introduction of Wilson term in the free fermion Lagrangian on lattice. The
Wilson-Yukawa chiral model on lattice is constructed by the generalized gauge
theory and a toy model and Smit-Swift model are studied.


title: A Dedicated Computer for Ising-like Spin Glass Models

abstract:
  We present a parallel machine, based on programmable devices, dedicated to
simulate spin glass models with Z2 variables and short range interaction. A
working prototype is described for two lattices containing 312x312 spins each
with an update time of 50 ns per spin. The final version of the three
dimensional parallel machine is discussed with spin update time up to 312 ps.


title:
Non-perturbative determination of the axial current normalization
  constant in O(a) improved lattice QCD

abstract:
  A finite-size technique is employed to compute the normalization constant
$Z_A$ of the isovector axial current in lattice QCD. The calculation is carried
out in the quenched approximation for values of the bare gauge coupling $g_0$
ranging from 0 to 1. In the lattice action and the lattice expression for the
axial current we include the counterterms required for O(a) improvement, with
non-perturbatively determined coefficients. With little additional work the
normalization constant $Z_V$ of the improved isospin current is also obtained.


title: Development in Lattice QCD

abstract:
  After a brief discussion of the promise and limitations of the lattice
technique, I review lattice QCD results for several quantities of
phenomenological interest. These are: matrix elements for heavy-to-light meson
decays, leptonic decay constants f_B and f_D, the parameters B_B and B_K for
neutral B and K meson mixing respectively, the strong coupling constant, light
quark masses and the lightest scalar glueball mass.


title: Cellular automata and self-organized criticality

abstract:
  Cellular automata provide a fascinating class of dynamical systems capable of
diverse complex behavior. These include simplified models for many phenomena
seen in nature. Among other things, they provide insight into self-organized
criticality, wherein dissipative systems naturally drive themselves to a
critical state with important phenomena occurring over a wide range of length
and time scales.


title: Self-organized criticality

abstract:
  I review the concept of self-organized criticality, wherein dissipative
systems naturally drive themselves to a critical state with important phenomena
occurring over a wide range of length and time scales. Several exact results
are demonstrated for the Abelian sandpile.


title: Better Actions

abstract:
  We explain why compact U(1) confines and how to fix it. We show that
plaquettes of negative trace carry most of the confinement signal in compact
SU(2). We show how to perform noncompact gauge-invariant simulations without
auxiliary fields. We suggest a way to simulate fermions without doublers.


title: Topology in 4D simplicial quantum gravity

abstract:
  We simulate 4d simplicial gravity for three topologis S4, S3xS1, (S1)^4 and
show that the free energy for these three fixed topology ensembles is the same
in the thermodynamic limit. We show, that the next-to-leading order
corrections, at least away from the critical point, can be described by
kinematic sources.


title: Light Quenched Hadron Spectrum and Decay Constants on different Lattices

abstract:
  In this paper we study O(2000) (quenched) lattice configurations from the APE
collaboration, for different lattice volumes and for 6.0 \le beta \le 6.4 using
both the Wilson and the SW-Clover fermion actions. We determine the light
hadronic spectrum and meson decay constants and study the mesonic dispersion
relation. We extract the hadronic variable J and the strange quark mass in the
continuum at the next-to-leading order obtaining m_s^{MSbar}(mu=2 GeV) = 122
+/- 20 MeV. A study is made of their dependence on lattice spacing. We
implement a newly developed technique to extract the inverse lattice spacing
using data at the simulated values of the quark mass (i.e. at masses around the
strange quark mass).


title: Reducing Discretization Errors in Lattice QCD Spectroscopy

abstract:
  The improved Wilson quark action - the clover action - is constructed to have
smaller discretization errors than the normal Wilson quark action. We test this
in a quenched spectroscopy computation on 6 lattice ensembles with spacings
from 0.15 to 0.43 fm. To ensure that the dominant scaling violations come from
the fermions we use an $O(a^2)$ improved 6-link $SU(3)$ pure gauge action. We
find evidence that fermionic scaling violations are consistent with $O(a^2)$
for clover fermions and $O(a)$ with a nonnegligible $O(a^2)$ term for standard
Wilson fermions. This latter mixed ansatz makes a reliable continuum
extrapolation problematic for Wilson fermions. For clover fermions, on the
other hand, we obtain accurate predictions for hadron masses in quenched
continuum QCD. We find that the slopes of the scaling violations are roughly
200 MeV for both Wilson and clover fermions.


title: Matrix Elements of 4-fermion Operators with Quenched Wilson Fermions

abstract:
  We presents results for the matrix elements of a variety of four-fermion
operators calculated using quenched Wilson fermions. Our simulations are done
on 170 lattices of size $32^3 x 64$ at $\beta = 6.0$. We find $B_K=0.74 +- 0.04
+- 0.05$, $B_D= 0.78 +- 0.01$, $B_7^{3/2}= 0.58 +- 0.02 {+0.07 \atop -0.03}$,
$B_8^{3/2}= 0.81 +- 0.03 {+.03 \atop -0.02}$, with all results being in the NDR
scheme at $\mu=2 GeV$. We also calculate the B-parameter for the operator
$\CQ_s$, which is needed in the study of the difference of B-meson lifetimes.
Our best estimate is $B_s(NDR,\mu=1/a)=0.80 +- 0.01$. This is given at the
lattice scale since the required 2-loop anomalous dimension matrix is not
known. In all these estimates, the first error is statistical, while the second
is due to the use of truncated perturbation theory to match continuum and
lattice operators. Errors due to quenching and lattice discretization are not
included. We also present new results for the perturbative matching
coefficients, extending the calculation to all Lorentz scalar four-fermion
operators, and using NDR as the continuum scheme.


title:
Topology at the Deconfinement Transition Uncovered by Inverse Blocking
  in SU(2) Pure Gauge Theory with Fixed Point Action

abstract:
  Renormalization group transformations as discussed recently in deriving fixed
point actions are used to analyse the vacuum structure near to the
deconfinement temperature. Monte Carlo configurations are generated using the
fixed point action. We compare equilibrium configurations with configurations
obtained by inverse blocking from a coarser lattice. The absence of short range
vacuum fluctuations in the latter does not influence the string tension. For
the inversely blocked configurations we find the following: (i) the topological
susceptibility chi_top is consistent with the phenomenological value in the
confinement phase, (ii) chi_top drops across the deconfinement transition,
(iii) density and size of instantons are estimated, (iv) the topological
density is found to be correlated to Abelian monopole currents and (v) the
density of spacelike monopole currents becomes a confinement order parameter.


title:
Ab Initio Calculation of Relativistic Corrections to the Static
  Interquark potential I: SU(2) Gauge Theory

abstract:
  We test the capability of state-of-the-art lattice techniques for a precise
determination of relativistic corrections to the static interquark potential,
by use of SU(2) gauge theory. Emphasis is put on the short range structure of
the spin dependent potentials, with lattice resolution a ranging from a approx
0.04 fm (at beta=2.74) down to a approx 0.02 fm (at beta=2.96) on volumes of
32^4 and 48^4 lattice sites. We find a new short range Coulomb-like
contribution to the spin-orbit potential V_1'.