title: Quarkonium spin structure in lattice NRQCD

abstract:
  Numerical simulations of the quarkonium spin splittings are done in the
framework of lattice nonrelativistic quantum chromodynamics (NRQCD). At leading
order in the velocity expansion the spin splittings are of $O(M_Q v^4)$, where
$M_Q$ is the renormalized quark mass and $v^2$ is the mean squared quark
velocity. A systematic analysis is done of all next-to-leading order
corrections. This includes the addition of $O(M_Q v^6)$ relativistic
interactions, and the removal of $O(a^2 M_Q v^4)$ discretization errors in the
leading-order interactions. Simulations are done for both S- and P-wave mesons,
with a variety of heavy quark actions and over a wide range of lattice
spacings. Two prescriptions for the tadpole improvement of the action are also
studied in detail: one using the measured value of the average plaquette, the
other using the mean link measured in Landau gauge. Next-to-leading order
interactions result in a very large reduction in the charmonium splittings,
down by about 60% from their values at leading order. There are further
indications that the velocity expansion may be poorly convergent for
charmonium. Prelimary results show a small correction to the hyperfine
splitting in the Upsilon system.


title:
Thermodynamics of the two--dimensional O(3) non linear sigma model with
  Fixed-Point lattice action

abstract:
  We calculate the free energy density of the two dimensional O(3) non linear
sigma model over a large temperature region. At high temperatures the
calculations could be done by perturbation theory whereas in the low
temperature regime we used Monte-Carlo simulations. Using the Fixed--Point
action the results do not show any remarkable cut-off effects and furthermore
the behaviour of these effects is nearly the same over the whole temperature
region. The results of the Fixed-Point action are then compared to those of the
standard Wilson action.


title: Scaling Behavior in 4D Simplicial Quantum Gravity

abstract:
  Scaling relations in four-dimensional simplicial quantum gravity are proposed
using the concept of the geodesic distance. Based on the analogy of a loop
length distribution in the two-dimensional case, the scaling relations of the
boundary volume distribution in four dimensions are discussed in three regions:
the strong-coupling phase, the critical point and the weak-coupling phase. In
each phase a different scaling behavior is found.


title:
Abelian projection and studies of gauge-variant quantities in lattice
  QCD without gauge fixing

abstract:
  We suggest a new (dynamical) Abelian projection of the lattice QCD. It
contains no gauge condition imposed on gauge fields so that Gribov copying is
avoided. Configurations of gauge fields that turn into monopoles in the Abelian
projection can be classified in a gauge invariant way. In the continuum limit,
the theory respects the Lorentz invariance. A similar dynamical reduction of
the gauge symmetry is proposed for studies of gauge-variant correlators (like a
gluon propagator) in lattice QCD. Though the procedure is harder for numerical
simulations, it is free of gauge fixing artifacts, like the Gribov horizon and
copies.


title: QCD with domain wall quarks

abstract:
  We present lattice calculations in QCD using a variant of Kaplan fermions
which retain the continuum SU(N)xSU(N) chiral symmetry on the lattice in the
limit of an infinite extra dimension. In particular, we show that the pion mass
and the four quark matrix element related to K_0-K_0-bar mixing have the
expected behavior in the chiral limit, even on lattices with modest extent in
the extra dimension, e.g. N_s=10.


title: Which Chiral Symmetry is Restored in High Temperature QCD?

abstract:
  Sigma models for the high temperature phase transition in quantum
chromodynamics (QCD) suggest that at high temperature the SU(N_f) x SU(N_f)
chiral symmetry becomes exact, but the anomalous axial U(1) symmetry need not
be restored. In numerical lattice simulations, traditional methods for
detecting symmetry restoration have sought multiplets in the screening mass
spectrum. However, these methods were imprecise and the results, so far,
incomplete. With improved statistics and methodology, we are now able to offer
evidence for a restoration of the SU(2) x SU(2) chiral symmetry just above the
crossover, but not of the axial U(1) chiral symmetry.


title: Quantum geometry of topological gravity

abstract:
  We study a c=-2 conformal field theory coupled to two-dimensional quantum
gravity by means of dynamical triangulations. We define the geodesic distance r
on the triangulated surface with N triangles, and show that dim[r^{d_H}]=
dim[N], where the fractal dimension d_H = 3.58 +/- 0.04. This result lends
support to the conjecture d_H = -2\alpha_1/\alpha_{-1}, where \alpha_{-n} is
the gravitational dressing exponent of a spin-less primary field of conformal
weight (n+1,n+1), and it disfavors the alternative prediction d_H =
-2/\gamma_{str}. On the other hand, we find dim[l] = dim[r^2] with good
accuracy, where l is the length of one of the boundaries of a circle with
(geodesic) radius r, i.e. the length l has an anomalous dimension relative to
the area of the surface. It is further shown that the spectral dimension d_s =
1.980 +/- 0.014 for the ensemble of (triangulated) manifolds used. The results
are derived using finite size scaling and a very efficient recursive sampling
technique known previously to work well for c=-2.


title: Critical properties and monopoles in U(1) lattice gauge theory

abstract:
  We present a detailed study of the properties of the phase transition in the
four-dimensional compact U(1) lattice gauge theory supplemented by a monopole
term, for values of the monopole coupling $\lambda$ such that the transition is
of second order. By a finite size analysis we show that at $\lambda= 0.9$ the
critical exponent is already characteristic of a second-order transition.
Moreover, we find that this exponent is definitely different from the one of
the Gaussian case. We further observe that the monopole density becomes
approximately constant in the second-order region. Finally we reveal the
unexpected phenomenon that the phase transition persists up to very large
values of $\lambda$, where the transition moves to (large) negative $\beta$.


title:
Questionable and unquestionable in the perturbation theory of
  non-Abelian models

abstract:
  We show, by explicit computation, that bare lattice perturbation theory in
the two-dimensional O(n) nonlinear $\sigma$ models with superinstanton boundary
conditions is divergent in the limit of an infinite number of points
$|\Lambda|$. This is the analogue of David's statement that renormalized
perturbation theory of these models is infrared divergent in the limit where
the physical size of the box tends to infinity. We also give arguments which
support the validity of the bare perturbative expansion of short-distance
quantities obtained by taking the limit $|\Lambda|\to\infty$ term by term in
the theory with more conventional boundary conditions such as Dirichlet,
periodic, and free.


title: Gluinos on the lattice: quenched calculations

abstract:
  As a preparation for the numerical study of the SU(2) gauge theory with
gluinos, the spectral properties of the fermion matrix and the masses of
pseudoscalar and scalar states are investigated in the quenched approximation.
The behaviour of the disconnected fermion diagrams on small lattices is also
studied.


title:
A Strong-Coupling Analysis of the Lattice $CP^{N-1}$ Models in the
  Presence of a $\theta$ Term

abstract:
  A $\theta$ term, which couples to topological charge, is added to the lattice
$CP^{N-1}$ model. The strong-coupling character expansion is developed. The
series for the free energy and mass gap are respectively computed to tenth
order and fourth order. Several features of the strong-coupling analysis
emerge. One is the loss of superconfinement. Another is that in the
intermediate coupling constant region, there are indications of a transition to
a deconfining phase when $\theta$ is sufficiently large. The transition is like
the one which has been observed in Monte Carlo simulations of a similar lattice
$CP^{N-1}$ action.


title: Improved Quark Actions for Lattice QCD

abstract:
  I present a brief summary of the status and prospects of improved Wilson-type
quark actions for coarse lattice simulations. My conclusions are optimistic.


title:
A Non-Perturbative Analysis of the Finite T Phase Transition in
  SU(2)xU(1) Electroweak Theory

abstract:
  The continuum 3d SU(2)$\times$U(1)+Higgs theory is an effective theory for a
large class of 4d high-temperature gauge theories, including the minimal
standard model and some of its supersymmetric extensions. We study the effects
of the U(1) subgroup using lattice Monte Carlo techniques. When $g'^2/g^2$ is
increased from the zero corresponding to pure SU(2)+Higgs theory, the phase
transition gets stronger. However, the increase in the strength is close to
what is expected perturbatively, and the qualitative features of the phase
diagram remain the same as for $g'^2=0$. In particular, the first order
transition still disappears for $m_H>m_{H,c}$. We measure the photon mass and
mixing angle, and find that the mass vanishes in both phases within the
statistical errors.


title: Perfect Lattice Actions for Staggered Fermions

abstract:
  We construct a perfect lattice action for staggered fermions by blocking from
the continuum. The locality, spectrum and pressure of such perfect staggered
fermions are discussed. We also derive a consistent fixed point action for free
gauge fields and discuss its locality as well as the resulting static
quark-antiquark potential. This provides a basis for the construction of
(classically) perfect lattice actions for QCD using staggered fermions.


title: Three-Dimensional 3-State Potts Model Revisited With New Techniques

abstract:
  We report a fairly detailed finite-size scaling analysis of the first-order
phase transition in the three-dimensional 3-state Potts model on cubic lattices
with emphasis on recently introduced quantities whose infinite-volume
extrapolations are governed `only' by exponentially small terms. In these
quantities no asymptotic power series in the inverse volume are involved which
complicate the finite-size scaling behaviour of standard observables related to
the specific-heat maxima or Binder-parameter minima. Introduced initially for
strong first-order phase transitions in q-state Potts models with ``large
enough'' q, the new techniques prove to be surprisingly accurate for a q value
as small as 3. On the basis of the high-precision Monte Carlo data of Alves `et
al.' [Phys. Rev. B43 (1991) 5846], this leads to a refined estimate of $\beta_t
= 0.550,565(10)$ for the infinite-volume transition point.


title:
How to Measure the Fractal Geometry of the Relativistic Fermion
  Propagator

abstract:
  We study the geometry of propagation of relativistic fermions. We propose how
to measure its quantum mechanical length. Numerical lattice results for the
free propagator of Dirac-Wilson fermions yield Hausdorff dimension d_H=2 for
the unit-matrix component and d_H=1 for any gamma-matrix component. A possible
generalization when matter interacts with radiation is discussed.


title:
Finite-Temperature Phase Structure of Lattice QCD with the Wilson Quark
  Action for Two and Four Flavors

abstract:
  We present further analyses of the finite-temperature phase structure of
lattice QCD with the Wilson quark action based on spontaneous breakdown of
parity-flavor symmetry. Results are reported on (i) an explicit demonstration
of spontaneous breakdown of parity-flavor symmetry beyond the critical line,
(ii) phase structure and order of chiral transition for the case of $N_f=4$
flavors, and (iii) approach toward the continuum limit.


title: Finite-Temperature QCD on the Lattice

abstract:
  Recent developments in finite-temperature studies of lattice QCD are
reviewed. Topics include (i) tests of improved actions for the pure gauge
system, (ii) scaling study of the two-flavor chiral transition and restoration
of $U_A(1)$ symmetry with the Kogut-Susskind quark action, (iii) present
understanding of the finite-temperature phase structure for the Wilson quark
action. New results for finite-density QCD are briefly discussed.


title:
Lattice Gauge Theory Simulations at Nonzero Chemical Potential in the
  Chiral Limit

abstract:
  We present a method of simulating lattice QCD at nonzero chemical potential
in the chiral limit. By adding a weak four-fermi interaction to the standard
staggered fermion SU(3) QCD action, we produce an algorithm in which the limit
of massless fermions is well-behaved and physical. Using configurations at zero
chemical potential, and an exact fugacity expansion of the fermion determinant,
we can simulate QCD at nonzero chemical potential and evade the notorious
problem of the complex action. Small lattice simulations give physical results:
At strong gauge coupling the critical chemical potential \mu_c agrees with
theoretical expectations and at weak gauge coupling \mu_c is nonzero in the low
temperature confined phase of QCD and jumps to zero in the high temperature
quark-gluon plasma phase. In all these simulations the quarks are exactly
massless and there is a Goldstone pion.


title: Improvements of the local bosonic algorithm

abstract:
  We report on several improvements of the local bosonic algorithm proposed by
M. Luescher. We find that preconditioning and over-relaxation works very well.
A detailed comparison between the bosonic and the Kramers-algorithms shows
comparable performance for the physical situation examined.


title: Krylov space solvers for shifted linear systems

abstract:
  We investigate the application of Krylov space methods to the solution of
shifted linear systems of the form (A+\sigma) x - b = 0 for several values of
\sigma simultaneously, using only as many matrix-vector operations as the
solution of a single system requires. We find a suitable description of the
problem, allowing us to understand known algorithms in a common framework and
developing shifted methods basing on short recurrence methods, most notably the
CG and the BiCGstab solvers. The convergence properties of these shifted
solvers are well understood and the derivation of other shifted solvers is
easily possible. The application of these methods to quark propagator
calculations in quenched QCD using Wilson and Clover fermions is discussed and
numerical examples in this framework are presented. With the shifted CG method
an optimal algorithm for staggered fermions is available.


title: QCDF90: Lattice QCD with Fortran 90

abstract:
  We have used Fortran 90 to implement lattice QCD. We have designed a set of
machine independent modules that define fields (gauge, fermions, scalars,
etc...) and overloaded operators for all possible operations between fields,
matrices and numbers. With these modules it is very simple to write high-level
efficient programs for QCD simulations. To increase performances our modules
also implements assignments that do not require temporaries, and a machine
independent precision definition. We have also created a useful compression
procedure for storing the lattice configurations, and a parallel implementation
of the random generators. We have widely tested our program and modules on
several parallel and single processor supercomputers obtaining excellent
performances.


title: Infrared Renormalons and Finite Volume

abstract:
  We analyze the perturbative expansion of a condensate in the O(N) non-linear
sigma model for large N on a two dimensional finite lattice. On an infinite
volume this expansion is affected by an infrared renormalon. We extrapolate
this analysis to the case of the gluon condensate of Yang-Mills theory and
argue that infrared renormalons can be detected by performing perturbative
studies even on relatively small lattices.


title: Lattice Formulation of the Standard Model

abstract:
  Combining the Kaplan surface mode approach for chiral fermions with added
terms motivated by Eichten and Preskill suggests the possibility for a lattice
regularization of the standard model which is finite, exactly gauge invariant,
and only has physically desired states in its low energy spectrum. The
conjectured scheme manifestly requires anomaly cancelation and explicitly
contains baryon and lepton number violating terms.


title: Thermodynamics of Four-Flavour QCD with Improved Staggered Fermions

abstract:
  We have calculated the pressure and energy density in four-flavour QCD using
improved fermion and gauge actions. We observe a strong reduction of finite
cut-off effects in the high temperature regime, similar to what has been noted
before for the SU(3) gauge theory. Calculations have been performed on
$16^3\times 4$ and 16^4 lattices for two values of the quark mass, $ma = 0.05$
and 0.1. A calculation of the string tension at zero temperature yields a
critical temperature $T_c/\sqrt{\sigma} = 0.407 \pm 0.010$ for the smaller
quark mass value.


title:
Structure of Critical Lines in Quenched Lattice QCD with the Wilson
  Quark Action

abstract:
  The structure of critical lines of vanishing pion mass for the Wilson quark
action is examined in quenched lattice QCD. The numerical evidence is presented
that critical lines spread into five branches beyond beta=5.6-5.7 at zero
temperature. It is also shown that critical lines disappear in the deconfined
phase for the case of finite temperatures.


title:
Thermodynamics of lattice QCD with two light quark flavours on a 16^3 x
  8 lattice II

abstract:
  We have extended our earlier simulations of the high temperature behaviour of
lattice QCD with two light flavours of staggered quarks on a $16^3 \times 8$
lattice to lower quark mass (m_q=0.00625). The transition from hadronic matter
to a quark-gluon plasma is observed at $6/g^2=5.49(2)$ corresponding to a
temperature of $T_c \approx 140$MeV. We present measurements of observables
which probe the nature of the quark-gluon plasma and serve to distinguish it
from hadronic matter. Although the transition is quite abrupt, we have seen no
indications that it is first order.


title: On the Phase Diagram of the SU(2) Adjoint Higgs Model in 2+1 Dimensions

abstract:
  The phase diagram is investigated for SU(2) lattice gauge theory in d=3,
coupled to adjoint scalars. For small values of the quartic scalar coupling,
lambda, the transition separating Higgs and confinement phases is found to be
first-order, in agreement with earlier work by Nadkarni. The surface of
second-order transitions conjectured by Nadkarni, however, is shown instead to
correspond to crossover behaviour. This conclusion is based on a finite size
analysis of the scalar mass and susceptibility. The nature of the phase
transition at the termination of first-order behaviour is investigated and we
find evidence for a critical point at which the scalar mass vanishes. The
photon mass and confining string tension are measured and are found to be
negligibly small in the Higgs phase. This is correlated with the very small
density of magnetic monopoles in the Higgs phase. The string tension and photon
mass rise rapidly as the crossover is traversed towards the symmetric phase.


title: Computer Aided Series Expansions for Critical Phenomena

abstract:
  Under quite general conditions critical phenomena can be described with high
order linked cluster expansions. The coefficients of the series admit a
graphical expansion that is generated with the aid of computers. Our
generalization of linked cluster expansions from an infinite to a finite volume
allows to perform a finite size scaling analysis. We also indicate a
generalization to Dynamical Linked Cluster Expansions with possible
applications to spin glasses and neural networks with coupled spin and
interaction dynamics.


title:
Four-dimensional Simulation of the Hot Electroweak Phase Transition with
  the SU(2) Gauge-Higgs Model

abstract:
  We study the finite-temperature electroweak phase transition of the minimal
standard model within the four-dimensional SU(2) gauge-Higgs model. Monte Carlo
simulations are performed for intermediate values of the Higgs boson mass in
the range $50 \lesssim M_H \lesssim 100$GeV on a lattice with the temporal size
$N_t=2$. The order of the transition is systematically examined using
finite-size scaling methods. Behavior of the interface tension and the latent
heat for an increasing Higgs boson mass is also investigated. Our results
suggest that the first-order transition terminates around $M_H \sim 80$GeV.


title: Measures of critical exponents in the four dimensional site percolation

abstract:
  Using finite-size scaling methods we measure the thermal and magnetic
exponents of the site percolation in four dimensions, obtaining a value for the
anomalous dimension very different from the results found in the literature. We
also obtain the leading corrections-to-scaling exponent and, with great
accuracy, the critical density.


title: The equation of state for two flavor QCD at N_t=6

abstract:
  We calculate the two flavor equation of state for QCD on lattices with
lattice spacing a=(6T)^{-1} and find that cutoff effects are substantially
reduced compared to an earlier study using a=(4T)^{-1}. However, it is likely
that significant cutoff effects remain. We fit the lattice data to expected
forms of the free energy density for a second order phase transition at
zero-quark-mass, which allows us to extrapolate the equation of state to m_q=0
and to extract the speed of sound. We find that the equation of state depends
weakly on the quark mass for small quark mass.


title:
Perturbation theory predictions and Monte Carlo simulations for the 2-d
  O(n) non-linear sigma-model

abstract:
  By using the results of a high-statistics (O(10^7) measurements) Monte Carlo
simulation we test several predictions of perturbation theory on the O(n)
non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on
large enough lattices to have a good control on finite-size effects. The
magnetic susceptibility and three different definitions of the correlation
length are measured. We check our results with large-n expansions as well as
with standard formulae for asymptotic freedom up to 4 loops in the standard and
effective schemes.
  For this purpose the weak coupling expansions of the energy up to 4 loops for
the standard action and up to 3 loops for the Symanzik action are calculated.
For the O(3) model we have used two different effective schemes and checked
that they lead to compatible results. A great improvement in the results is
obtained by using the effective scheme based on the energy at 3 and 4 loops. We
find that the O(8) model follows very nicely (within few per mille) the
perturbative predictions. For the O(3) model an acceptable agreement (within
few per cent) is found.

categories: hep-lat comp-gas cond-mat hep-th nlin.CG nlin.SI solv-int


title: Computation of the one-loop Symanzik coefficients for the square action

abstract:
  We compute the one-loop coefficients for an alternative Symanzik improved
pure gauge SU{N} lattice action (N=2 and N=3). For the standard Symanzik
improved action we confirm previous results by L\"{u}scher and Weisz.


title: SU(N) gauge theories for all N in 3 and 4 dimensions

abstract:
  We compare the mass spectra and string tensions of SU(2), SU(3) and SU(4)
gauge theories in 2+1 dimensions. We find that the ratios of masses are, to a
first approximation, independent of N and that the remaining dependence can be
accurately reproduced by a simple O(1/N^2) correction. This provides us with a
prediction of these mass ratios for all SU(N) theories in 2+1 dimensions and
demonstrates that these theories are `close' to N=\infty for N\geq 2. We also
find that, when expressed in units of the dynamical length scale of the theory,
the dimensionful coupling g^2 is proportional to 1/N at large N. We confirm
that these theories are indeed confining in the limit N \to \infty. We describe
preliminary calculations in 3+1 dimensions which indicate that the same will be
true there.


title: SU(N) gauge theories for all N

abstract:
  We show that SU(N) gauge theories in 2+1 dimensions are close to N=\infty for
N \geq 2. The dimensionful coupling, g^2, is proportional to 1/N, at large N,
confirming the usual diagram-based expectation. Preliminary calculations in 3+1
dimensions indicate that the same is true there.


title: Gauge-ball spectrum of the four-dimensional pure U(1) gauge theory

abstract:
  We investigate the continuum limit of the gauge-ball spectrum in the
four-dimensional pure U(1) lattice gauge theory. In the confinement phase we
identify various states scaling with the correlation length exponent $\nu
\simeq 0.35$. The square root of the string tension also scales with this
exponent, which agrees with the non-Gaussian fixed point exponent recently
found in the finite size studies of this theory. Possible scenarios for
constructing a non-Gaussian continuum theory with the observed gauge-ball
spectrum are discussed. The $0^{++}$ state, however, scales with a Gaussian
value $\nu \simeq 0.5$. This suggests the existence of a second, Gaussian
continuum limit in the confinement phase and also the presence of a light or
possibly massless scalar in the non-Gaussian continuum theory. In the Coulomb
phase we find evidence for a few gauge-balls, being resonances in multi-photon
channels; they seem to approach the continuum limit with as yet unknown
critical exponents. The maximal value of the renormalized coupling in this
phase is determined and its universality confirmed.


title: Quantum geometry of 2d gravity coupled to unitary matter

abstract:
  We show that there exists a divergent correlation length in 2d quantum
gravity for the matter fields close to the critical point provided one uses the
invariant geodesic distance as the measure of distance. The corresponding
reparameterization invariant two-point functions satisfy all scaling relations
known from the ordinary theory of critical phenomena and the KPZ exponents are
determined by the power-like fall off of these two-point functions. The only
difference compared to flat space is the appearance of a dynamically generated
fractal dimension d_h in the scaling relations. We analyze numerically the
fractal properties of space-time for Ising and three-states Potts model coupled
to 2d dimensional quantum gravity using finite size scaling as well as small
distance scaling of invariant correlation functions. Our data are consistent
with d_h=4, but we cannot rule out completely the conjecture d_H =
-2\alpha_1/\alpha_{-1}, where \alpha_{-n} is the gravitational dressing
exponent of a spin-less primary field of conformal weight (n+1,n+1). We compute
the moments <L^n> and the loop-length distribution function and show that the
fractal properties associated with these observables are identical, with good
accuracy, to the pure gravity case.


title: Universal Amplitude Ratios in the 3D Ising Model

abstract:
  We present a high precision Monte Carlo study of various universal amplitude
ratios of the three dimensional Ising spin model. Using state of the art
simulation techniques we studied the model close to criticality in both phases.
Great care was taken to control systematic errors due to finite size effects
and correction to scaling terms. We obtain $C_+/C_-=4.75(3)$,
$f_{+,2nd}/f_{-,2nd}=1.95(2)$ and $u^*=14.3(1)$. Our results are compatible
with those obtained by field theoretic methods applied to the $\phi^4$ theory
and high and low temperature series expansions of the Ising model. The mismatch
with a previous Montecarlo study by Ruge et al. remains to be understood.


title: On Lattice QCD with Many Flavors

abstract:
  We discuss the confining and chiral-symmetry breaking properties of QCD with
a large number of flavors $N_f$. In a Monte Carlo simulation of QCD with $N_f
=16$ staggered fermions, we find clear evidence of a first order bulk phase
transition which separates phases with broken and unbroken chiral symmetry.
This is consistent with extrapolations of earlier studies with smaller $N_f$,
and is also as expected from general arguments. Thus, even when the
perturbative renormalization group flow has a new infrared stable fixed point
near the origin, lattice artifacts induce chiral symmetry breaking, and
presumably confinement, at sufficiently strong coupling.


title: Faster Fermions in the Tempered Hybrid Monte Carlo Algorithm

abstract:
  Tempering is used to change the quark mass while remaining in equilibrium
between the trajectories of a standard hybrid Monte Carlo simulation of four
flavours of staggered fermions. The algorithm is faster for small enough quark
masses, and particularly so when more than one mass is required.


title:
Random Walk Representation of the Lattice Fermionic Propagators and the
  Quark Model

abstract:
  A representation of the continuum fermionic propagator as a sum of directed
random walks on a lattice is presented. Also a random walk representation for
the lattice fermionic propagators is developed for the case of the naive, the
Wilson, and the Kogut-Susskind fermions. For the naive fermions the phenomenon
of fermion doubling appears as having $2^{D}$ distinct spin factors being
associated with a single path in $D$-dimensions. In the case of the Wilson and
the Kogut-Susskind fermions, in the naive continuum limit, the path integral
representation coincides with the path integral representation for the
continuum fermionic propagator. Using this representation the Green's functions
of lattice QCD involving quark operators are written as a sum over the paths of
valence quark, the gauge fields and the sea quarks being integrated out.
Possible advantages of such a representation are illustrated by showing how one
can use numerical simulations to obtain a heuristic insight into the
relationship between QCD and the constituent quark model.


title: Monte Carlo Study of Pure-Phase Cumulants of 2D q-State Potts Models

abstract:
  We performed Monte Carlo simulations of the two-dimensional q-state Potts
model with q=10, 15, and 20 to study the energy and magnetization cumulants in
the ordered and disordered phase at the first-order transition point $\beta_t$.
By using very large systems of size 300 x 300, 120 x 120, and 80 x 80 for q=10,
15, and 20, respectively, our numerical estimates provide practically (up to
unavoidable, but very small statistical errors) exact results which can serve
as a useful test of recent resummed large-q expansions for the energy cumulants
by Bhattacharya `et al.' [J. Phys. I (France) 7 (1997) 81]. Up to the third
order cumulant and down to q=10 we obtain very good agreement, and also the
higher-order estimates are found to be compatible.


title: Topology of the SU(2) vacuum: a lattice study using improved cooling

abstract:
  We study the topological structure of the SU(2) vacuum at zero temperature:
topological susceptibility, size, shape and distance distributions of the
instantons. We use a cooling algorithm based on an improved action with scale
invariant instanton solutions. This algorithm needs no monitoring or
calibration, has an inherent cut off for dislocations and leaves unchanged
instantons at physical scales. The physical relevance of our results is checked
by studying the scaling and finite volume dependence. We obtain a
susceptibility of (200(15) MeV)^4. The instanton size distribution is peaked
around 0.43fm, and the distance distribution indicates a homogeneous, random
spatial structure.


title:
Four-Dimensional N=1 Supersymmetric Yang-Mills Theory on the Lattice
  without Fine-Tuning

abstract:
  We propose a method to formulate four-dimensional N=1 super Yang-Mills theory
on the lattice without fine-tuning. We first show that four-dimensional Weyl
fermion in a real representation, which is equivalent to Majorana fermion, can
be formulated using the domain wall approach with an addition of a Majorana
mass term only for the unwanted mirror fermion. This formalism has manifest
gauge invariance. Fermion number conservation is violated only by the
additional Majorana mass term for the mirror fermion and the violation is
propagated to the physical fermion sector through anomalous currents. Due to
this feature, the formalism, when applied to the gluino in the present case,
ensures the restoration of supersymmetry in the continuum limit without
fine-tuning, unlike the proposal by Curci and Veneziano.


title: The Svetitsky-Yaffe conjecture for the plaquette operator

abstract:
  According to the Svetitsky-Yaffe conjecture, a (d+1)-dimensional pure gauge
theory undergoing a continuous deconfinement transition is in the same
universality class as a d-dimensional statistical model with order parameter
taking values in the center of the gauge group. We show that the plaquette
operator of the gauge theory is mapped into the energy operator of the
statistical model. For d=2, this identification allows us to use conformal
field theory techniques to evaluate exactly the correlation functions of the
plaquette operator at the critical point. In particular, we can evaluate
exactly the plaquette expectation value in presence of static sources, which
gives some new insight in the structure of the color flux tube in mesons and
baryons.


title:
Series Expansions for the Massive Schwinger Model in Hamiltonian lattice
  theory

abstract:
  It is shown that detailed and accurate information about the mass spectrum of
the massive Schwinger model can be obtained using the technique of
strong-coupling series expansions. Extended strong-coupling series for the
energy eigenvalues are calculated, and extrapolated to the continuum limit by
means of integrated differential approximants, which are matched onto a
weak-coupling expansion. The numerical estimates are compared with exact
results, and with finite-lattice results calculated for an equivalent lattice
spin model with long-range interactions. Both the heavy fermion and the light
fermion limits of the model are explored in some detail.


title: The Three Dimensional Thirring Model for Small N_f

abstract:
  We formulate the three dimensional Thirring model on a spacetime lattice and
study it for various even numbers of fermion flavors N_f by Monte Carlo
simulation. We find clear evidence for spontaneous chiral symmetry breaking at
strong coupling, contradicting the predictions of the 1/N_f expansion. The
critical point appears to correspond to an ultra-violet fixed point of the
renormalisation group; a fit to a RG-inspired equation of state in the vicinity
of the fixed point yields distinct critical exponents for N_f=2 and N_f=4,
while no fit is found for N_f=6, suggesting there is a critical number N_fc<6
beyond which no chiral symmetry breaking occurs. The spectrum of the N_f=2
theory is studied; the states examined vary sharply but continuously across the
transition.


title:
Scaling of cluster fluctuations in two-dimensional q=5 and 7 state Potts
  models

abstract:
  The scaling behavior of fluctuations in cluster size is studied in q=5 and 7
state Potts models. This quantity exhibits scaling behavior on small lattices
where the scaling of local operators like energy fluctuations and Binder
cumulant can not be expected.


title: Study of Cluster Fluctuations in Two-dimensional q-State Potts Model

abstract:
  The two-dimensional Potts Model with 2 to 10 states is studied using a
cluster algorithm to calculate fluctuations in cluster size as well as commonly
used quantities like equilibrium averages and the histograms for energy and the
order parameter. Results provide information about the variation of cluster
sizes depending on the temperature and the number of states. They also give
evidence for first-order transition when energy and the order parameter related
measurables are inconclusive on small size lattices.


title:
A toy model test of a new algorithm for bozonization of fermion
  determinants

abstract:
  Different aspects of bozonization algorithm proposed by Slavnov are tested by
numerical simulations of a one dimensional toy model.


title: Monte Carlo Study of the 3D Thirring Model

abstract:
  I review three different non-perturbative approaches to the three dimensional
Thirring model: the 1/N_f expansion, Schwinger-Dyson equations, and Monte Carlo
simulation. Simulation results are presented to support the existence of a
non-perturbative fixed point at a chiral symmetry breaking phase transition for
N_f=2 and 4, but not for N_f=6. Spectrum calculations for $N_f=2$ reveal
conventional level ordering near the transition.


title:
Coexistence of monopoles and instantons for different topological charge
  definitions and lattice actions

abstract:
  We compute instanton sizes and study correlation functions between instantons
and monopoles in maximum abelian projection within SU(2) lattice QCD at finite
temperature. We compare several definitions of the topological charge,
different lattice actions and methods of reducing quantum fluctuations. The
average instanton size turns out to be $\sigma \approx 0.2$ fm. The correlation
length between monopoles and instantons is $\zeta \approx 0.25$ fm and hardly
affected by lattice artifacts as dislocations. We visualize several specific
gauge field configurations and show directly that there is an enhanced
probability for finding monopole loops in the vicinity of instantons. This
feature is independent of the topological charge definition used.


title: A numerical test of the continuum index theorem on the lattice

abstract:
  The overlap formalism of chiral fermions provides a tool to measure the
index, Q, of the chiral Dirac operator in a fixed gauge field background on the
lattice. This enables a numerical measurement of the probability distribution,
p(Q), in Yang-Mills theories. We have obtained an estimate for p(Q) in pure
SU(2) gauge theory by measuring Q on 140 independent gauge field configurations
generated on a 12^4 lattice using the standard single plaquette Wilson action
at a coupling of beta=2.4. This distribution is in good agreement with a recent
measurement [8] of the distribution of the topological charge on the same
lattice using the same coupling and the same lattice gauge action. In
particular we find <Q^2>=3.3(4) to be compared with <Q^2> = 3.9(5) found in
[8]. The good agreement between the two distributions is an indication that the
continuum index theorem can be carried over in a probabilistic sense on to the
lattice.


title: Instantons and monopoles in lattice QCD

abstract:
  We analyze the interplay of topological objects in four-dimensional QCD on
the lattice. The distributions of color magnetic monopoles in the maximum
abelian gauge are computed around instantons in both pure and full QCD. We find
an enhanced probability for monopoles inside the core of an instanton on gauge
field average. This feature is independent of the topological charge definition
used. For specific gauge field configurations we visualize the situation
graphically. Moreover we investigate how monopole loops and instantons are
correlated with the chiral condensate. Strong evidence is found that clusters
of the quark condensate and topological objects coexist locally on individual
configurations.


title:
Possible evidence for the mass shift of $\eta$' meson at finite
  temperature

abstract:
  Topological charge distributions of SU(3) gauge theory at finite temperature
are calculated on the lattice with high statistics in a manner of free from the
uncertainty of $\beta$-function. Clear temperature dependence of the
topological charge distribution is obtained. Combining the present result with
the recent study about the relation between the masses of $\eta$ meson system
and the gauge field topology, we obtain $m_{\eta'}(T)/m_{\eta'}(0) = 0.86 \pm
0.02$ and $0.69 \pm 0.01$ for $T=0.75 T_c$ and $T=0.93 T_c$, respectively. The
result shows the first clear evidence of the mass shift of $\eta'$ meson at
finite temperature.


title:
Questionable Arguments for the Correctness of Perturbation Theory in
  Non-Abelian Models

abstract:
  We analyze the arguments put forward recently by Niedermayer et al in favor
of the correctness of conventional perturbation theory in non-Abelian models
and supposedly showing that our super-instanton counterexample was sick. We
point out that within their own set of assumptions, the proof of Niedermayer et
al regarding the correctness of perturbation theory is incorrect and provide a
correct proof under more restrictive assumptions. We reply also to their claim
that the S-matrix bootstrap approach of Balog et al supports the existence of
asymptotic freedom in the O(3) model.


title: Fermionic Monte Carlo algorithms for lattice QCD

abstract:
  The increase with time of computer resources devoted to simulations of full
QCD is spectacular. Yet the reduction of systematic errors is comparatively
slow. This is due to the algorithmic complexity of the problem. I review, in
elementary terms, the origin of this complexity, and estimate it for 3 exact
fermion algorithms.


title:
On the evaluation of universal non-perturbative constants in O(N) sigma
  models

abstract:
  We investigate the relation between on-shell and zero-momentum
non-perturbative quantities entering the parametrization of the two-point
Green's function of two-dimensional non-linear O(N) sigma models. We present
accurate estimates of ratios of mass-scales and renormalization constants,
obtained by an analysis of the strong-coupling expansion of the two-point
Green's function. These ratios allow to connect exact known on-shell results
with typical zero-momentum lattice evaluations. Our results are supported by
the 1/N-expansion.


title: Z(3) Interfaces in Lattice Gauge Theory

abstract:
  A study is made of properties of the Z(3) interface which forms between the
different ordered phases of pure SU(3) gauge theory above a critical
temperature. The theory is simulated on a (2+1)-D lattice at various
temperatures above this critical point. At high temperatures, the interface
tension is shown to agree well with the prediction of perturbation theory. Near
the critical temperature, the interface behaviour is characterised by various
displacement moments, and modelled by an interacting scalar field theory. This
thesis is provided for reference, as it gives full details of the computational
and statistical methods outlined only briefly in preprints hep-lat/9605040 and
hep-lat/9607005.


title: Monopoles and deconfinement transition in SU(2) lattice gauge theory

abstract:
  We investigate SU(2) lattice gauge theory in four dimensions in the maximally
abelian projection. Studying the effects on different lattice sizes we show
that the deconfinement transition of the fields and the percolation transition
of the monopole currents in the three space dimensions are precisely related.
To arrive properly at this result the uses of a mathematically sound
characterization of the occurring networks of monopole currents and of an
appropriate method of gauge fixing turn out to be crucial. In addition we
investigate detailed features of the monopole structure in time direction.


title: On-shell improved lattice QCD with staggered fermions

abstract:
  By using Symanzik's improvement program, we study on-shell improved lattice
QCD with staggered fermions. We find that there are as many as 15 independent
lattice operators of dimension of six~(including both gauge and fermion
operators) which must be added to the unimproved action to form an $O(a^2)$
improved action. Among them, the total number of dimension-6 gauge operators
and fermion bilinears is 5. The other 10 terms are four-fermion operators. At
the tree-level and tadpole-improved tree-level, all the 10 four fermion
operators are absent.


title: Quark Confinement in C-periodic Cylinders at Temperatures above T_c

abstract:
  Due to the Gauss law, a single quark cannot exist in a periodic volume, while
it can exist with C-periodic boundary conditions. In a C-periodic cylinder of
cross section A = L_x L_y and length L_z >> L_x, L_y containing deconfined
gluons, regions of different high temperature Z(3) phases are aligned along the
z-direction, separated by deconfined- deconfined interfaces. In this geometry,
the free energy of a single static quark diverges in proportion to L_z. Hence,
paradoxically, the quark is confined, although the temperature T is larger than
T_c. At T around T_c, the confined phase coexists with the three deconfined
phases. The deconfined-deconfined interfaces can be completely or incompletely
wet by the confined phase. The free energy of a quark behaves differently in
these two cases. In contrast to claims in the literature, our results imply
that deconfined-deconfined interfaces are not Euclidean artifacts, but have
observable consequences in a system of hot gluons.


title:
Chiral perturbation theory for K+ to pi+ pi0 decay in the continuum and
  on the lattice

abstract:
  In this paper we use one-loop chiral perturbation theory in order to compare
lattice computations of the K+ to pi+ pi0 decay amplitude with the experimental
value. This makes it possible to investigate three systematic effects that
plague lattice computations: quenching, finite-volume effects, and the fact
that lattice computations have been done at unphysical values of the quark
masses and pion external momenta (only this latter effect shows up at tree
level). We apply our results to the most recent lattice computation, and find
that all three effects are substantial. We conclude that one-loop corrections
in chiral perturbation theory help in explaining the discrepancy between
lattice results and the real-world value. We also revisit B_K, which is closely
related to the K+ to pi+ pi0 decay amplitude by chiral symmetry.


title: A Polynomial Hybrid Monte Carlo Algorithm

abstract:
  We present a simulation algorithm for dynamical fermions that combines the
multiboson technique with the Hybrid Monte Carlo algorithm. We find that the
algorithm gives a substantial gain over the standard methods in practical
simulations. We point out the ability of the algorithm to treat fermion
zeromodes in a clean and controllable manner.


title: Numerical study of plasmon properties in the SU(2)-Higgs model

abstract:
  Using the (effective) classical approximation, we compute numerically
time-dependent correlation functions in the SU(2)-Higgs model around the
electroweak phase transition, for $m_H \approx m_W$. The parameters of the
classical model have been determined previously by the dimensional reduction
relations for time-independent correlators. The $H$ and $W$ correlation
functions correspond to gauge invariant fields. They show damped oscillatory
behavior from which we extract frequencies $\om$ and damping rates $\gm$. In
the Higgs phase the damping rates have roughly the values obtained in analytic
calculations in the quantum theory. In the plasma phase (where analytic
estimates for gauge invariant fields are not available), the damping rate
associated with $H$ is an order of magnitude larger than in the Higgs phase,
while the $W$ correlator appears to be overdamped, with a small rate. The
frequency $\om_H$ shows a clear dip at the transition. The results are
approximately independent of the lattice spacing, but this appears to be
compatible with the lattice spacing dependence expected from perturbation
theory.


title: Phase Structures of U(2) Gauge Theory with $\theta$-Term in 2 dimensions

abstract:
  U(2) lattice gauge theory with $\theta$-term in 2 space-time dimensions is
investigated. It has non-Abelian real action and Abelian( U(1) type) imaginary
action. The imaginary action is defined as the standard $\theta$-term. As the
effect of renormalization group (RG) transformation, non-Abelian imaginary
action is induced. After many steps of RG transformation, non-Abelian part will
die away. After several steps of RG transformations, renormalized action
approaches so called heat kernel action. Phase transition is found at $\theta
=\pi$ only.


title: Pion loops in quenched Quantum Chromodynamics

abstract:
  We calculate the divergences of the generating functional of quenched Chiral
Perturbation Theory to one loop for a generic number of flavours. The flavour
number dependence of our result enlightens the mechanism of quark loop
cancellation in the quenched effective theory for any Green function or S
matrix element. We also apply our results to $\pi \pi$ scattering and evaluate
the coefficient of the chiral log in the S-wave scattering lengths for the
quenched case.


title:
Measuring the interface tension when the electroweak phase transition
  becomes weak

abstract:
  We measure the interface tension near the phase transition endpoint of the 3d
SU(2)-Higgs model. The tunnel correlation length method is used and compared to
other approaches. A modified scaling behaviour for the mass gap as function of
the transverse area is proposed.


title: The Higgs mechanism on the lattice

abstract:
  The lattice regularization of the Higgs sector of the standard model is
summarized. The triviality bound and vacuum instability bound are described.
The question of chiral gauge theories is discussed. Some aspects of the
numerical simulations of the electroweak phase transition are considered.


title:
A High Statistics Lattice Calculation of Heavy-Light Meson Decay
  Constants

abstract:
  We present a high statistics study of the D- and B-meson decay constants. The
results were obtained by using the Clover and Wilson lattice actions at two
different values of the lattice spacing $a$, corresponding to $\beta=6.0$ and
6.2. After a careful analysis of the systematic errors present in the
extraction of the physical results, by assuming quite conservative
discretization errors, we find $f_{D_s}=237 \pm 16$ MeV, $f_{D} = 221 \pm 17$
MeV ($f_{D_s}/f_D=1.07(4)$), $f_{B_s} = 205 \pm 35$ MeV, $f_{B} = 180 \pm 32$
MeV ($f_{B_s}/f_B=1.14(8)$), in good agreement with previous estimates.


title: QCD Thermodynamics with an Improved Lattice Action

abstract:
  We have investigated QCD with two flavors of degenerate fermions using a
Symanzik-improved lattice action for both the gauge and fermion actions. Our
study focuses on the deconfinement transition on an $N_t=4$ lattice. Having
located the thermal transition, we performed zero temperature simulations
nearby in order to compute hadronic masses and the static quark potential. We
find that the present action reduces lattice artifacts present in
thermodynamics with the standard Wilson (gauge and fermion) actions. However,
it does not bring studies with Wilson-type quarks to the same level as those
using the Kogut--Susskind formulation.


title: Three-dimensional lattice U(1) gauge-Higgs model at low $m_H$

abstract:
  We study the non-compact version of the U(1) gauge-Higgs model in three
dimensions for $m_H = 30 GeV.$ We found that, using this formulation, rather
modest lattices approach quite well the infinite volume behaviour.The phase
transition is first order, as expected for this Higgs mass. The latent heat (in
units of $T_{cr}^4$) is compatible with the predictions of the two-loop
effective potential; it is an order of magnitude less than the corresponding
SU(2) value. The transition temperature and $<\varphi^* \varphi>$ in units of
the critical temperature are also compatible with the perturbative results.


title: Hubbard Model with L\"uscher fermions

abstract:
  We study the basic features of the two-dimensional quantum Hubbard Model at
half-filling by means of the L\"uscher algorithm and the algorithm based on
direct update of the determinant of the fermionic matrix. We implement the
L\"uscher idea employing the transfer matrix formalism which allows to
formulate the problem on the lattice in $(2+1)$ dimensions. We discuss the
numerical complexity of the L\"uscher technique, systematic errors introduced
by polynomial approximation and introduce some improvements which reduce long
autocorrelations. In particular we show that preconditioning of the fermionic
matrix speeds up the algorithm and extends the available range of parameters.
We investigate the magnetic and the one-particle properties of the Hubbard
Model at half-filling and show that they are in qualitative agreement with the
existing Monte Carlo data and the mean-field predictions.


title:
Fermion determinants in matrix models of QCD at nonzero chemical
  potential

abstract:
  The presence of a chemical potential completely changes the analytical
structure of the QCD partition function. In particular, the eigenvalues of the
Dirac operator are distributed over a finite area in the complex plane, whereas
the zeros of the partition function in the complex mass plane remain on a
curve. In this paper we study the effects of the fermion determinant at nonzero
chemical potential on the Dirac spectrum by means of the resolvent, G(z), of
the QCD Dirac operator. The resolvent is studied both in a one-dimensional U(1)
model (Gibbs model) and in a random matrix model with the global symmetries of
the QCD partition function. In both cases we find that, if the argument z of
the resolvent is not equal to the mass m in the fermion determinant, the
resolvent diverges in the thermodynamic limit. However, for z =m the resolvent
in both models is well defined. In particular, the nature of the limit $z
\rightarrow m$ is illuminated in the Gibbs model. The phase structure of the
random matrix model in the complex m and \mu-planes is investigated both by a
saddle point approximation and via the distribution of Yang-Lee zeros. Both
methods are in complete agreement and lead to a well-defined chiral condensate
and quark number density.


title:
On the Path Integral Loop Representation of (2+1) Lattice Non-Abelian
  Theory

abstract:
  A gauge invariant Hamiltonian representation for SU(2) in terms of a spin
network basis is introduced. The vectors of the spin network basis are
independent and the electric part of the Hamiltonian is diagonal in this
representation. The corresponding path integral for SU(2) lattice gauge theory
is expressed as a sum over colored surfaces, i.e. only involving the $j_p$
attached to the lattice plaquettes. This surfaces may be interpreted as the
world sheets of the spin networks In 2+1 dimensions, this can be accomplished
by working in a lattice dual to a tetrahedral lattice constructed on a face
centered cubic Bravais lattice. On such a lattice, the integral of gauge
variables over boundaries or singular lines -- which now always bound three
coloured surfaces -- only contributes when four singular lines intersect at one
vertex and can be explicitly computed producing a 6-j or Racah symbol. We
performed a strong coupling expansion for the free energy. The convergence of
the series expansions is quite different from the series expansions which were
performed in ordinary cubic lattices. In the case of ordinary cubic lattices
the strong coupling expansions up to the considered truncation number of
plaquettes have the great majority of their coefficients positive, while in our
case we have almost equal number of contributions with both signs. Finally, it
is discused the connection in the naive coupling limit between this action and
that of the B-F topological field theory and also with the pure gravity action.


title: String tension in gonihedric 3D Ising models

abstract:
  For the 3D gonihedric Ising models defined by Savvidy and Wegner the bare
string tension is zero and the energy of a spin interface depends only on the
number of bends and self-intersections, in antithesis to the standard
nearest-neighbour 3D Ising action. When the parameter kappa weighting the
self-intersections is small the model has a first order transition and when it
is larger the transition is continuous.
  In this paper we investigate the scaling of the renormalized string tension,
which is entirely generated by fluctuations, using Monte Carlo simulations This
allows us to obtain an estimate for the critical exponents alpha and nu using
both finite-size-scaling and data collapse for the scaling function.


title: Finite Temperature Quark Confinement

abstract:
  Confinement may be more easily demonstrated at finite temperature using the
Polyakov loop than at zero temperature using the Wilson loop. A natural
mechanism for confinement can arise via the coupling of the adjoint Polyakov
loop to F_{mu nu}^2. We demonstrate this mechanism with a one-loop calculation
of the effective potential for SU(2) gluons in a background field consisting of
a non-zero color magnetic field and a non-trivial Polyakov loop. The color
magnetic field drives the Polyakov loop to non-trivial behavior, and the
Polyakov loop can remove the well-known tachyonic mode associated with the
Saviddy vacuum. Minimizing the real part of the effective potential leads to
confinement, as determined by the Polyakov loop. Unfortunately, we cannot
arrange for simultaneous stability and confinement for this simple class of
field configurations. We show for a large class of abelian background fields
that at one loop tachyonic modes are necessary for confinement.


title: Further Precise Determinations of $\alpha_s$ from Lattice QCD

abstract:
  We present a new determination of the strong coupling constant from lattice
QCD simulations. We use four different short-distance quantities to obtain the
coupling, three different (infrared) meson splittings to tune the simulation
parameters, and a wide range of lattice spacings, quark masses, and lattice
volumes to test for systematic errors. Our final result consists of ten
different determinations of $\alpha^{(3)}_{P}(8.2 GeV)$, which agree well with
each other and with our previous results. The most accurate of these, when
evolved perturbatively to the $Z^0$ mass, gives $\alpha^{(5)}_{\msbar}(M_Z) =
.1174(24)$. We compare our results with those obtained from other recent
lattice simulations.


title: Getting Around the Nielsen-Ninomiya Theorem, towards the Rome Approach

abstract:
  The ``no-go'' theorem of Nielsen and Ninomiya has been the most tenacious
obstacle against the construction of a chiral gauge theory with reasonable low
energy spectrum, couplings and anomaly. In this paper we construct a model
which supplements the usual (bilinear in the Fermi fields) lagrangian with
quadrilinear fermionic terms. We show that in a certain region of the parameter
space the difficulties of the ``no-go'' theorem may be overcome, and a
``renormalized'' perturbative strategy can be carried out, akin to the one
followed in the Rome Approach (RA), whose counterterms are forced to be gauge
invariant.


title: Monopoles contra vortices in SU(2) lattice gauge theory?

abstract:
  We show that the scenario of vortex induced confinement of center--projected
SU(2) lattice gauge theory is not necessarily in conflict with the findings in
the positive plaquette model.


title: The Wiener-Hermite expansions of the Langevin transitions

abstract:
  New partial differential equations for the Wiener-Hermite expansions of the
Langevin (stochastic) transitions are formulated. They are solved recursively
in full order series solutions with respect to $\sqrt{t}$. A sort of 'gauge'
degrees of freedom (arbitrariness) involved in the solutions are analyzed and
clarified. The Wiener-Hermite expansions play important roles as basic elements
of numerical simulations of the Langevin equations. Specific solutions within
some orders are presented as examples. These expansions giving integral
representations of the Fokker-Planck evolution kernels, similar formulations
are possible for the imaginary time Hamiltonian evolution kernels as well.


title: Pion and Rho Structure Functions from Lattice QCD

abstract:
  We calculate the lower moments of the deep-inelastic structure functions of
the pion and the rho meson on the lattice. Of particular interest to us are the
spin-dependent structure functions of the rho. The calculations are done with
Wilson fermions and for three values of the quark mass, so that we can perform
an extrapolation to the chiral limit.


title:
Does Conformal Quantum Field Theory Describe the Continuum Limits of 2D
  Spin Models with Continuous Symmetry?

abstract:
  It is generally taken for granted that two-dimensional critical phenomena can
be fully classified by the well known two-dimensional (rational) conformal
quantum field theories (CQFTs). In particular it is believed that in models
with a continuous symmetry characterized by a Lie group $G$ the continuum
theory enjoys an enhanced symmetry $G\times G$ due to the decoupling of right
and left movers. In this letter we review the conventional arguments leading to
this conclusion, point out two gaps and provide a conterexample. Nevertheless
we justify in the end the conventional conclusions by additional arguments.


title:
Continuum Limit of $2D$ Spin Models with Continuous Symmetry and
  Conformal Quantum Field Theory

abstract:
  According to the standard classification of Conformal Quantum Field Theory
(CQFT) in two dimensions, the massless continuum limit of the $O(2)$ model at
the Kosterlitz-Thouless (KT) transition point should be given by the massless
free scalar field; in particular the Noether current of the model should be
proportional to (the dual of) the gradient of the massless free scalar field,
reflecting a symmetry enhanced from $O(2)$ to $O(2)\times O(2)$. More
generally, the massless continuum limit of a spin model with a symmetry given
by a Lie group $G$ should have an enhanced symmetry $G\times G$. We point out
that the arguments leading to this conclusion contain two serious gaps: i) the
possibility of `nontrivial local cohomology' and ii) the possibility that the
current is an ultralocal field. For the $2D$ $O(2)$ model we give analytic
arguments which rule out the first possibility and use numerical methods to
dispose of the second one. We conclude that the standard CQFT predictions
appear to be borne out in the $O(2)$ model, but give an example where they
would fail. We also point out that all our arguments apply equally well to any
$G$ symmetric spin model, provided it has a critical point at a finite
temperature.


title:
The 2n-point renormalized coupling constants in the 3d Ising model:
  estimates by high temperature series to order beta^17

abstract:
  We compute the 2n-point renormalized coupling constants in the symmetric
phase of the 3d Ising model on the sc lattice in terms of the high temperature
expansions O(beta^{17}) of the Fourier transformed 2n-point connected
correlation functions at zero momentum. Our high temperature estimates of these
quantities, which enter into the small field expansion of the effective
potential for a 3d scalar field at the IR fixed point or, equivalently, in the
critical equation of state of the 3d Ising model universality class, are
compared with recent results obtained by renormalization group methods, strong
coupling, stochastic simulations as well as previous high temperature
expansions.


title:
N-vector spin models on the sc and the bcc lattices: a study of the
  critical behavior of the susceptibility and of the correlation length by high
  temperature series extended to order beta^{21}

abstract:
  High temperature expansions for the free energy, the susceptibility and the
second correlation moment of the classical N-vector model [also known as the
O(N) symmetric classical spin Heisenberg model or as the lattice O(N) nonlinear
sigma model] on the sc and the bcc lattices are extended to order beta^{21} for
arbitrary N. The series for the second field derivative of the susceptibility
is extended to order beta^{17}. An analysis of the newly computed series for
the susceptibility and the (second moment) correlation length yields updated
estimates of the critical parameters for various values of the spin
dimensionality N, including N=0 [the self-avoiding walk model], N=1 [the Ising
spin 1/2 model], N=2 [the XY model], N=3 [the Heisenberg model]. For all values
of N, we confirm a good agreement with the present renormalization group
estimates. A study of the series for the other observables will appear in a
forthcoming paper.


title:
Complete O(v^2) corrections to the static interquark potential from
  SU(3) gauge theory

abstract:
  For the first time, we determine the complete spin- and momentum-dependent
order v^2 corrections to the static interquark potential from simulations of
QCD in the valence quark approximation at inverse lattice spacings of 2-3 GeV.
A new flavor dependent correction to the central potential is found. We report
a 1/r^2 contribution to the long range spin-orbit potential V_1'. The other
spin-dependent potentials turn out to be short ranged and can be well
understood by means of perturbation theory. The momentum-dependent potentials
qualitatively agree with minimal area law expectations. In view of spectrum
calculations, we discuss the matching of the effective nonrelativistic theory
to QCD as well as renormalization of lattice results. In a first survey of the
resulting bottomonia and charmonia spectra we reproduce the experimental levels
within average errors of 12.5 MeV and 22 MeV, respectively.


title:
Non-Perturbative Evaluation of the Physical Classical Velocity in the
  Lattice Heavy Quark Effective Theory

abstract:
  In the lattice formulation of the Heavy Quark Effective Theory, the value of
the classical velocity v, as defined through the separation of the 4-momentum
of a heavy quark into a part proportional to the heavy quark mass and a
residual part which remains finite in the heavy quark limit (P = Mv + p) is
different from its value as it appears in the bare heavy quark propagator (S(p)
= 1/vp). The origin of the difference, which is effectively a lattice-induced
renormalization, is the reduction of Lorentz (or O(4)) invariance to
(hyper)-cubic invariance. The renormalization is finite and depends
specifically on the form of the discretization of the reduced heavy quark Dirac
equation. For the Forward Time - Centered Space discretization, we compute this
renormalization non-perturbatively, using an ensemble of lattices at beta = 6.1
provided by the Fermilab ACP-MAPS Collaboration. The calculation makes crucial
use of a variationally optimized smeared operator for creating composite
heavy-light mesons. It has the property that its propagator achieves an
asymptotic plateau in just a few Euclidean time steps. For comparison, we also
compute the shift perturbatively, to one loop in lattice perturbation theory.
The non-perturbative calculation of the leading multiplicative shift in the
classical velocity is considerably different from the one-loop estimate, and
indicates that for the above parameters, v is reduced by about 10-13%.


title:
Further results on O(a) improved lattice QCD to one-loop order of
  perturbation theory

abstract:
  We present results at one-loop order of perturbation theory for various
improvement coefficients in on-shell O($a$) improved lattice QCD. In particular
we determine the additive counterterm required for on-shell improvement of the
isovector vector current. Employing a general mass-independent renormalization
scheme we also obtain the coefficients of the O($a$) counterterms which are
proportional to the quark mass in the improved isovector pseudo-scalar, axial
vector and vector operators. In the latter case a comparison with a recent
non-perturbative study is made.


title: Quenched Hadron Spectrum and Decay Constants on the lattice

abstract:
  In this talk we present the results obtained from a study of ${\cal O}(2000)$
(quenched) lattice configurations from the APE collaboration, at
$6.0\le\beta\le 6.4$, using both the Wilson and the SW-Clover fermion action.
We determine the light hadronic spectrum and the meson decay constants. For the
light-light systems 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.
For the heavy-light decay constants we find $f_{D_s}=237 \pm 16 MeV, f_{D} =
221 \pm 17 MeV (f_{D_s}/f_D=1.07(4)), f_{B_s} = 205 \pm 35 MeV, f_{B} = 180 \pm
32 MeV (f_{B_s}/f_B=1.14(8))$, in good agreement with previous estimates.


title: Toward numerical and analytical studies of first order phase transitions

abstract:
  Discrete lattice simulations of an one-dimensional phi^4 theory coupled to an
external heat bath are being carried out. Great care is taken to remove the
effects of lattice discreteness and finite size and to establish the correct
correspondence between simulations and the desired, finite-temperature
continuum limit.


title:
Running coupling constant of background perturbation theory and lattice
  interquark interaction

abstract:
  The conventional parametrizations of lattice static interquark force are
shown to produce a mismatch of coupling constant near the matching point R_m
\approx 0.2 fm. The running coupling constant of the background perturbation
theory yields instead a selfconsistent description of lattice data over all
interval of distances, 0.05 fm \la R \la 1.1.fm, and is an analytic function
with the property of asymptotic freedom at small R and it is freezing at large
R.


title: How to Count Kinks: From the Continuum to the Lattice and Back

abstract:
  We investigate the matching between (1+1)-dimensional nonlinear field
theories coupled to an external stochastic environment and their lattice
simulations. In particular, we focus on how to obtain numerical results which
are lattice-spacing independent, and on how to extract the correct effective
potential which emerges from the simulations. As an application, we study the
thermal production of kink-antikink pairs, obtaining a number density of pairs
which is lattice-spacing independent and the effective barrier for pair
production, i.e., the effective kink mass.

categories: hep-lat cond-mat.stat-mech hep-ph nlin.PS patt-sol


title:
Scaling and confinement aspects of tadpole improved SU(2) lattice gauge
  theory and its abelian projection

abstract:
  Using a tadpole improved SU(2) gluodynamics action, the nonabelian potential
and the abelian potential after the abelian projection are computed. Rotational
invariance is found restored at coarse lattices both in the nonabelian theory
and in the effective abelian theory resulting from maximal abelian projection.
Asymptotic scaling is tested for the SU(2) string tension. Deviation of the
order of $6%$ is found, for lattice spacings between 0.27 and 0.06 fm. Evidence
for asymptotic scaling and scaling of the monopole density in maximal abelian
projection is also seen, but not at coarse lattices. The scaling behavior is
compared with analyses of Wilson action results, using bare and renormalized
coupling schemes. Using extended monopoles, evidence is found that the gauge
dependence of the abelian projection reflects short distance fluctuations, and
may thus disappear at large scales.


title: Random matrix triality at nonzero chemical potential

abstract:
  We introduce three universality classes of chiral random matrix ensembles
with a nonzero chemical potential and real, complex or quaternion real matrix
elements. In the thermodynamic limit we find that the distribution of the
eigenvalues in the complex plane does not depend on the Dyson index, and is
given by the solution proposed by Stephanov. For a finite number of degrees of
freedom, $N$, we find an accumulation of eigenvalues on the imaginary axis for
real matrices, whereas for quaternion real matrices we find a depletion of
eigenvalues in this domain. This effect is of order $1/\sqrt N$. In particular
for the real case the resolvent shows a discontinuity of order $1/\sqrt N$.
These results are in agreement with lattice QCD simulations with staggered
fermions and recent instanton liquid simulations both for two colors and
nonzero chemical potential.


title:
Heavy-Light Mesons with Quenched Lattice NRQCD: Results on Decay
  Constants

abstract:
  We present a quenched lattice calculation of heavy-light meson decay
constants, using non-relativistic (NRQCD) heavy quarks in the mass region of
the $b$ quark and heavier, and clover-improved light quarks. The NRQCD
Hamiltonian and the heavy-light current include the corrections at first order
in the expansion in the inverse heavy quark mass. We study the dependence of
the decay constants on the heavy meson mass $M$, for light quarks with the tree
level ($c_{SW}$ = 1), as well as the tadpole improved clover coefficient. We
compare decay constants from NRQCD with results from clover ($c_{SW}=1$) heavy
quarks.
  Having calculated the current renormalisation constant $Z_A$ in one-loop
perturbation theory, we demonstrate how the heavy mass dependence of the
pseudoscalar decay constants changes after renormalisation. For the first time,
we quote a result for $f_B$ from NRQCD including the full one-loop matching
factors at $O(\alpha/M)$.


title: Cluster algorithms

abstract:
  Cluster algorithms for classical and quantum spin systems are discussed. In
particular, the cluster algorithm is applied to classical O(N) lattice actions
containing interactions of more than two spins. The performance of the
multi-cluster and single--cluster methods, and of the standard and improved
estimators are compared. (Lecture given at the summer school on `Advances in
Computer Simulations', Budapest, July 1996.)


title: Finite density QCD with chiral invariant four-fermion interactions

abstract:
  A mean field analysis of finite density QCD is presented including the
effects of additional chiral invariant four-fermion interactions. A lattice
regularization is used with N_f=4 flavors of staggered fermions. The use of the
four-fermion coupling as an improved extrapolation parameter over the bare
quark mass in Monte Carlo simulations is discussed. Particular attention is
given to the structure of the phase diagram and the order of the chiral phase
transition. At zero gauge coupling, the model reduces to a Nambu-Jona-Lasinio
model. In this limit the chiral phase transition is found to be second-order
near the zero-density critical point and otherwise first-order. In the strong
gauge coupling limit a first-order chiral phase transition is found. In this
limit the additional four-fermion interactions do not qualitatively change the
physics. The results agree with previous studies of QCD as the four-fermion
coupling vanishes.


title: Efficient glueball simulations on anisotropic lattices

abstract:
  Monte Carlo results for the low-lying glueball spectrum using an improved,
anisotropic action are presented. Ten simulations at lattice spacings ranging
from 0.2 to 0.4 fm and two different anisotropies have been performed in order
demonstrate the advantages of using coarse, anisotropic lattices to calculate
glueball masses. Our determinations of the tensor (2++) and pseudovector (1+-)
glueball masses are more accurate than previous Wilson action calculations.


title: The Coulomb law in the pure gauge U(1) theory on a lattice

abstract:
  We study the heavy charge potential in the Coulomb phase of pure gauge
compact U(1) theory on the lattice. We calculate the static potential
$V_W(T,{\vec R})$ from Wilson loops on a $16^3 \times 32$ lattice and compare
with the predictions of lattice perturbation theory. We investigate finite size
effects and, in particular, the importance of non-Coulomb contributions to the
potential. We also comment on the existence of a maximal coupling in the
Coulomb phase of pure gauge U(1) theory.


title: Where the electroweak phase transition ends

abstract:
  We give a more precise characterisation of the end of the electroweak phase
transition in the framework of the effective 3d SU(2)--Higgs lattice model than
has been given before. The model has now been simulated at gauge couplings
beta_G=12 and 16 for Higgs masses M_H^*=70, 74, 76 and 80 GeV up to lattices
96^3 and the data have been used for reweighting. The breakdown of finite
volume scaling of the Lee-Yang zeroes indicates the change from a first order
transition to a crossover at lambda_3/g_3^2=0.102(2) in rough agreement with
results of Karsch et al (hep-lat/9608087) at \beta_G=9 and smaller lattices.
The infinite volume extrapolation of the discontinuity Delta < phi^+ phi >
/g_3^2 turns out to be zero at lambda_3/g_3^2=0.107(2) being an upper limit. We
comment on the limitations of the second method.


title:
Lattice Artefacts In The Non-Abelian Debye Screening Mass In One Loop
  Order

abstract:
  We compute the electric screening mass in lattice QCD with Wilson fermions at
finite temperature and chemical potential to one-loop order, and show that
lattice artefacts arising from a finite lattice spacing result in an
enhancement of the screening mass as compared to the continuum. We discuss the
magnitude of this enhancement as a function of the temperature and chemical
potential for lattices with different number of lattice sites in the temporal
direction that can be implemented in lattice simulations. Most of the
enhancement is found to be due to the fermion loop contribution.


title: Perfect Lattice Topology: The Quantum Rotor as a Test Case

abstract:
  Lattice actions and topological charges that are classically and quantum
mechanically perfect (i.e. free of lattice artifacts) are constructed
analytically for the quantum rotor. It is demonstrated that the Manton action
is classically perfect while the Villain action is quantum perfect. The
geometric construction for the topological charge is only perfect at the
classical level. The quantum perfect lattice topology associates a topological
charge distribution, not just a single charge, with each lattice field
configuration. For the quantum rotor with the classically perfect action and
topological charge, the remaining cut-off effects are exponentially suppressed.


title: Monte Carlo Studies of Two-Dimensional Systems with a $\theta$ Term

abstract:
  A $\theta$ term, which couples to topological charge, is added to the
two-dimensional lattice CP^3 model and U(1) gauge theory. Monte Carlo
simulations are performed and compared to strong-coupling character expansions.
In certain instances, a flattening behavior occurs in the free-energy at
sufficiently large $\theta$, but the effect is an artifact of the simulation
methods.


title: Improving the signal-to-noise-ratio in lattice gauge theories

abstract:
  Renormalization of composite fields is employed to suppress the statistical
noise in lattice gauge calculations. We propose a new action which differs from
the standard Wilson action by ''irrelevant'' operators, but suppresses the
fluctuations of the plaquette. We numerically study the Creutz ratios and find
a scaling window. The SU(2) mass gap is estimated. We prove that the
contributions of the ''irrelevant'' operators to the screening mass decrease
towards the continuum limit. The results obtained from the action with noise
suppression are compared with those of the standard Wilson action.


title: Microscopic universality in the spectrum of the lattice Dirac operator

abstract:
  Large ensembles of complete spectra of the Euclidean Dirac operator for
staggered fermions are calculated for SU(2) lattice gauge theory. The
accumulation of eigenvalues near zero is analyzed as a signal of chiral
symmetry breaking and compared with parameter-free predictions from chiral
random matrix theory. Excellent agreement for the distribution of the smallest
eigenvalue and the microscopic spectral density is found. This provides direct
evidence for the conjecture that these quantities are universal functions.


title: Light Quark Masses with Dynamical Wilson Fermions

abstract:
  We determine the masses of the light and the strange quarks in the
$\bar{MS}$-scheme using our high-statistics lattice simulation of QCD with
dynamical Wilson fermions. For the light quark mass we find
$m^{light}_{\bar{MS}}(2 GeV) = 2.7(2) MeV$, which is lower than in quenched
simulations. For the strange quark, in a sea of two dynamical light quarks, we
obtain $m^{strange}_{\bar{MS}}(2 GeV) = 140(20) MeV$.


title: Potts Models on Feynman Diagrams

abstract:
  We investigate numerically and analytically Potts models on ``thin'' random
graphs -- generic Feynman diagrams, using the idea that such models may be
expressed as the N --> 1 limit of a matrix model. The thin random graphs in
this limit are locally tree-like, in distinction to the ``fat'' random graphs
that appear in the planar Feynman diagram limit, more familiar from discretized
models of two dimensional gravity.
  The interest of the thin graphs is that they give mean field theory behaviour
for spin models living on them without infinite range interactions or the
boundary problems of genuine tree-like structures such as the Bethe lattice.
q-state Potts models display a first order transition in the mean field for
q>2, so the thin graph Potts models provide a useful test case for exploring
discontinuous transitions in mean field theories in which many quantities can
be calculated explicitly in the saddle point approximation.


title: Aharonov-Bohm Effect in Lattice Abelian Higgs Theory

abstract:
  We study a field-theoretical analogue of the Aharonov-Bohm effect in two-,
three- and four-dimensional Abelian Higgs models; the corresponding topological
interaction is proportional to the linking number of the Abrikosov vortex and
the particle world trajectories. We show that the Aharonov-Bohm effect gives
rise to a nontrivial interaction of charged test particles. The numerical
calculations in the three-dimensional model confirm this fact.


title: Domain wall fermions with Majorana couplings

abstract:
  We examine the lattice boundary formulation of chiral fermions with either an
explicit Majorana mass or a Higgs-Majorana coupling introduced on one of the
boundaries. We demonstrate that the low-lying spectrum of the models with an
explicit Majorana mass of the order of an inverse lattice spacing is chiral at
tree level. Within a mean-field approximation we show that the systems with a
strong Higgs-Majorana coupling have a symmetric phase, in which a Majorana mass
of the order of an inverse lattice spacing is generated without spontaneous
breaking of the gauge symmetry. We argue, however, that the models within such
a phase have a chiral spectrum only in terms of the fermions that are singlets
under the gauge group. The application of such systems to nonperturbative
formulations of supersymmetric and chiral gauge theories is briefly discussed.


title: Quenched Approximation Artifacts: A study in 2-dimensional QED

abstract:
  The spectral properties of the Wilson-Dirac operator in 2-dimensional QED
responsible for the appearance of exceptional configurations in quenched
simulations are studied in detail. The mass singularity structure of the
quenched functional integral is shown to be extremely compicated, with multiple
branch points and cuts. The connection of lattice topological charge and
exactly real eigenmodes is explored using cooling techniques. The lattice
volume and spacing dependence of these modes is studied, as is the effect of
clover improvement of the action. A recently proposed modified quenched
approximation is applied to the study of meson correlators, and the results
compared with both naive quenched and full dynamical calculations of the same
quantity.


title: Lattice-continuum relations for 3d SU(N)+Higgs theories

abstract:
  3d lattice studies have recently attracted a lot of attention, especially in
connection with finite temperature field theories. One ingredient in these
studies is a perturbative computation of the 2-loop lattice counterterms, which
are exact in the continuum limit. We extend previous such results to SU(N)
gauge theories with Higgs fields in the fundamental and adjoint
representations. The fundamental SU(3)xSU(2) case might be relevant for the
electroweak phase transition in the MSSM, and the adjoint case for the GUT
phase transition and for QCD in the high temperature phase. We also revisit the
standard SU(2)xU(1) and U(1) theories.


title:
Singularities of the Partition Function for the Ising Model Coupled to
  2d Quantum Gravity

abstract:
  We study the zeros in the complex plane of the partition function for the
Ising model coupled to 2d quantum gravity for complex magnetic field and real
temperature, and for complex temperature and real magnetic field, respectively.
We compute the zeros by using the exact solution coming from a two matrix model
and by Monte Carlo simulations of Ising spins on dynamical triangulations. We
present evidence that the zeros form simple one-dimensional curves in the
complex plane, and that the critical behaviour of the system is governed by the
scaling of the distribution of the singularities near the critical point.
Despite the small size of the systems studied, we can obtain a reasonable
estimate of the (known) critical exponents.


title:
Gribov Copies in the Minimal Landau Gauge: the Influence on Gluon and
  Ghost Propagators

abstract:
  We study the influence of Gribov copies on gluon and ghost propagators,
evaluated numerically in pure SU(2) lattice gauge theory in the minimal Landau
gauge. Simulations are done at four different values of $\beta$ (namely $\beta$
= 0, 0.8, 1.6 and 2.7) and for volumes up to $16^4$ (up to $24^4$ at $\beta$ =
1.6). For the gluon propagator, Gribov noise seems to be of the order of
magnitude of the numerical accuracy, even at very small values of the coupling
$\beta$. On the contrary, for the ghost propagator, Gribov noise is clearly
observable for the three values of $\beta$ in the strong-coupling regime. In
particular, data corresponding to the minimal Landau gauge are always smaller
than those obtained in a generic Landau gauge. This result can be qualitatively
explained.


title: Monte Carlo evaluation of a fermion number violating observable in 2D

abstract:
  We describe in some detail a computer evaluation of a 't Hooft vertex in a
two dimensional model using the overlap. The computer result agrees with the
known exact continuum value, and in this sense our work is a first successful
fully dynamical simulation of a chiral gauge theory on the lattice. We add some
new data to numbers obtained earlier and provide a selfcontained description
which should make it easy for others to reproduce and follow up on our work.


title:
Ising description of the transition region in SU(3) gauge theory at
  finite temperature

abstract:
  We attempt the numerical construction of an effective action in three
dimensions for Ising spins which represent the Wilson lines in the
four-dimensional SU(3) gauge theory at finite temperature. For each
configuration of the gauge theory, each spin is determined by averaging the
Wilson lines over a small neighborhood and then projecting the average to +/-1
according to whether the neighborhood is ordered or disordered. The effective
Ising action, determined via the lattice Schwinger-Dyson equations, contains
even (two-spin) and odd (one- and three-spin) terms with short range. We find
that the truncation to Ising degrees of freedom produces an effective action
which is discontinuous across the gauge theory's phase transition. This
discontinuity may disappear if the effective action is made more elaborate.


title: Light Quarks, Zero Modes, and Exceptional Configurations

abstract:
  In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues
of the massless Dirac operator. In lattice QCD with Wilson fermions, these zero
modes appear as exactly real eigenvalues of the Wilson-Dirac operator and hence
as poles in the quark propagator in the vicinity of critical hopping parameter.
It is shown that "exceptional configurations" which arise in the quenched
approximation at small quark mass are the result of the fluctuation of the
position of zero mode poles to sub-critical values of the hopping parameter on
particular gauge configurations. We describe a procedure for correcting these
lattice artifacts by first isolating the contribution of zero mode poles to the
quark propagator and then shifting the sub-critical poles to the critical
point. This procedure defines a modified quenched approximation in which
accurate calculations can be carried out for arbitrarily small quark masses.


title: Topological Structure in the SU(2) Vacuum

abstract:
  We study the topological content of the vacuum of SU(2) pure gauge theory
using lattice simulations. We use a smoothing process based on the
renormalization group equation which removes short distance fluctuations but
preserves long distance structure. The action of the smoothed configurations is
dominated by instantons, but they still show an area law for Wilson loops with
a string tension equal to the string tension on the original configurations.
Yet it appears that instantons are not directly responsible for confinement.
The average radius of an instanton is about 0.2 fm, at a density of about 2
fm^(-4). This is a much smaller average size than other lattice studies have
indicated. The instantons appear not to be randomly distributed in space, but
are clustered.


title: Mass Gap, Abelian Dominance and Vortex Dynamics in SU(2) Spin Model

abstract:
  We discuss a new approach to the investigation of the nature of the mass gap
in spin systems with continuous global symmetries which is much analogous to
the method of abelian projection in the gauge theories. We suggest that the
abelian degrees of freedom, in particular, abelian vortices are responsible for
the mass gap generation phenomena in the non-abelian spin systems. To check our
hypothesis we study numerically the three-dimensional SU(2) spin model in the
Maximal Abelian projection. We find that the abelian mass gap in the projected
theory coincides with the full non-abelian mass gap within numerical errors.
The study of the percolation properties of the abelian vortex trajectories
shows that the phase transition and the mass gap generation in the 3D SU(2)
spin model are driven by the abelian vortex condensation.


title: Brief Review of Multicanonical Simulations

abstract:
  Recent progress of simulations with non-canonical weight factors is
summarized.


title: The Schr\"odinger functional running coupling with staggered fermions

abstract:
  We discuss the Schr\"odinger functional in lattice QCD with staggered
fermions including its order $O(a)$ boundary counterterms. We relate it, in the
classical continuum limit, to the Schr\"odinger functional as obtained in the
same limit with Wilson fermions. We compute the strong coupling constant
defined via the Schr\"odinger functional with staggered fermions at one loop
and show that it agrees with the continuum running coupling constant in the
Schr\"odinger functional formalism.


title: Exotic hadronic states and all-to-all quark propagators

abstract:
  We discuss methods to obtain accurate hadronic spectra with propagating
quarks. Comparing the determination of masses for spin-exotic hybrid mesons
with glueball mass determinations, we conclude that quark propagators from all
sites to all other sites would enable great improvement in the errors. Such
propagators are achievable by using stochastic estimators. We discuss previous
attempts and present our method for maximal variance reduction. This is a very
promising technique and we illustrate it by obtaining the spectrum of ground
state and excited B mesons in the limit where the $b$ quark is static.


title:
Continuous Chiral Transition in Strongly Coupled Compact QED with the
  Standard Torus Topology

abstract:
  We analyze the phase diagram of compact QED on the torus with a chirally
symmetric four fermion interaction added to the usual Wilson action. Inside a
mean field approximation for the four fermion term, a line of first order phase
transitions and another one of second order are found in the $(\beta, G)$
plane. Approaching the second order line a continuum limit can be defined.
Critical exponents vary along this line in a similar way as in the non-compact
model, suggesting that a non trivial interacting continuum theory can be
constructed.


title:
Logarithmic Corrections to the Equation of State in the SU(2)xSU(2)
  Nambu - Jona-Lasinio Model

abstract:
  We present results from a Monte Carlo simulation of the Nambu - Jona-Lasinio
model, with continuous SU(2)xSU(2) chiral symmetry, in four Euclidean
dimensions. Different model equations of state, corresponding to different
theoretical scenarios, are tested against the order parameter data. The results
are sensitive to necessary assumptions about the shape and extent of the
scaling region. Our best fits favour a trivial scenario in which the
logarithmic corrections are qualitatively similar to those predicted by the
large N_f approximation. This is supported by a separate analysis of finite
volume corrections for data taken directly in the chiral limit.


title:
Status and Perspective of Non-perturbative Renormalization in Weak
  Decays

abstract:
  We discuss the status and the problems related to the application of the
off-shell non-perturbative renormalization method in a fixed gauge to operators
relevant to weak decays. In particular, we critically reappraise the method
recently proposed for the $\Delta I=1/2$ rule. We also present a general
analysis of the renormalization for the $\Delta I=3/2$ operators, and apply it
to the $\Delta S=2$ operator.


title: B Meson Decay Constants Using NRQCD

abstract:
  Recent results for B meson decay constants with NRQCD b-quarks and clover
light quarks are discussed. Perturbative matching factors through O($\alpha/M$)
are now available and incorporated into the analyses. An O($\alpha a$)
improvement term to the heavy-light axial current is identified and included.
The slope of $f_{PS}\sqrt{M_{PS}}$ versus $1/M_{PS}$ is significantly reduced
by these corrections.


title: Non-perturbative improvement of composite operators with Wilson fermions

abstract:
  We propose a method to improve lattice operators composed of Wilson fermions
which allows the removal of all corrections of $O(a)$, including those
proportional to the quark mass, leaving only errors of $O(a^2)$. The method
exploits the fact that chiral symmetry is restored at short distances. By
imposing this requirement on correlation functions of improved lattice
operators at short distances, the coefficients which appear in these operators
can be determined. The method is an extension of the improvement program of the
ALPHA collaboration, which, up to now, has only been applicable in the chiral
limit. The extension to quarks with non-zero masses is particularly important
for applications in heavy quark physics.


title:
Investigating Confinement in Dually Transformed U(1) Lattice Gauge
  Theory

abstract:
  The dually transformed path integral of four-dimensional U(1) lattice gauge
theory is used for the calculation of expectation values in the presence of
external charges. Applying the dual simulation to flux tubes for charge
distances up to around 20 lattice spacings, we find a deviation from the
behaviour of a dual type-II superconductor in the London limit at large
distances. The roughening of the flux tube agrees with the effective string
picture of confinement. Further we show that finite temperature effects are
negligible for time extents larger than the charge distance. Finally we analyze
the different contributions to the total energy of the electromagnetic field.
The parallel component of the magnetic field turns out to have the strongest
influence on the deviation from the linear behaviour at small charge distances.


title: Random Surfaces in Three-Dimensional Simplicial Gravity

abstract:
  A model of simplicial quantum gravity in three dimensions is investigated
numerically based on the technique of the dynamical triangulation (DT). We are
concerned with the surfaces appearing on boundaries (i.e., sections) of
three-dimensional DT manifold with $S^{3}$ topology. A new scaling behavior of
genus distributions of boundary surfaces is found.Furthermore, these surfaces
are compared with the random surfaces generated by the two-dimensional DT
method which are well known as a correct discretized method of the
two-dimensional quantum gravity.


title: Optimization of Monte-Carlo calculations of the effective potential

abstract:
  We study Monte Carlo calculations of the effective potential for a scalar
field theory using three techniques. One of these is a new method proposed and
tested for the first time. In each case we extract the renormalised quantities
of the theory. The system studied in our calculations is a one component
$\phi^4$ model in two dimensions. We apply these methods to both the weak and
strong coupling regime. In the weak coupling regime we compare our results for
the renormalised quantities with those obtained from two-loop lattice
perturbation theory. Our results are verified in the strong coupling regime
through comparison with the strong coupling expansion. We conclude that
effective potential methods, when suitably chosen, can be accurate tools in
calculations of the renormalised parameters of scalar field theories.


title:
Comments on ``Lattice Formulation of the Standard Model'' by Creutz. et.
  al

abstract:
  The main construction of the paper in the title [hep-lat/9612017] is
summarized using more standard particle physics language. Also, a flaw is
pointed out and several objections to the more general thoughts expressed by
Creutz et. al. are raised.


title:
Chiral Symmetry Restoration in the Schwinger Model with Domain Wall
  Fermions

abstract:
  Domain Wall Fermions utilize an extra space time dimension to provide a
method for restoring the regularization induced chiral symmetry breaking in
lattice vector gauge theories even at finite lattice spacing. The breaking is
restored at an exponential rate as the size of the extra dimension increases.
Before this method can be used in dynamical simulations of lattice QCD, the
dependence of the restoration rate to the other parameters of the theory and,
in particular, the lattice spacing must be investigated. In this paper such an
investigation is carried out in the context of the two flavor lattice Schwinger
model.


title:
Gauge Freedom in Chiral Gauge Theory with Vacuum Overlap --
  Two-dimensional case

abstract:
  Dynamical nature of the gauge degree of freedom and its effect to fermion
spectrum are studied at $\beta=\infty$ for two-dimensional nonabelian chiral
gauge theory in the vacuum overlap formulation. It is argue that the disordered
gauge degree of freedom does not necessarily cause the massless chiral state in
the (waveguide) boundary correlation function. An asymptotically free
self-coupling for the gauge degree of freedom is introduced by hand at first.
This allows us to tame the gauge fluctuation by approaching the critical point
of the gauge degree of freedom without spoiling its disordered nature. We
examine the spectrum in the boundary correlation function and find the mass gap
of the order of the lattice cutoff. There is no symmetry against it. Then we
argue that the decoupling of the gauge freedom can occur as the self-coupling
is removed, provided that the IR fixed point due to the Wess-Zumino term is
absent by anomaly cancellation.