title: Abelian Dominance in Chiral Symmetry Breaking

abstract:
  Calculations of the chiral condensate $\langle \bar{\psi} \psi \rangle$ on
the lattice using staggered fermions and the Lanczos algorithm are presented.
Three gauge fields are considered: the quenched non-Abelian field, the Abelian
field projected in the maximal Abelian gauge, and the monopole field further
decomposed from the Abelian field. The results show that the Abelian monopoles
largely reproduce the chiral condensate values of the full non-Abelian theory,
both in SU(2) and in SU(3).


title:
An Accelerated Conjugate Gradient Algorithm to Compute Low-Lying
  Eigenvalues --- a Study for the Dirac Operator in SU(2) Lattice QCD

abstract:
  The low-lying eigenvalues of a (sparse) hermitian matrix can be computed with
controlled numerical errors by a conjugate gradient (CG) method. This CG
algorithm is accelerated by alternating it with exact diagonalisations in the
subspace spanned by the numerically computed eigenvectors. We study this
combined algorithm in case of the Dirac operator with (dynamical) Wilson
fermions in four-dimensional $\SUtwo$ gauge fields. The algorithm is
numerically very stable and can be parallelized in an efficient way. On
lattices of sizes $4^4-16^4$ an acceleration of the pure CG method by a factor
of~$4-8$ is found.


title:
Electroweak Phase Transition and Numerical Simulations in the SU(2)
  Higgs Model

abstract:
  Recent progress in non-perturbative investigations of the electroweak phase
transition is reviewed, with special emphasis on numerical simulations in the
four-dimen\-sional SU(2) Higgs model.


title: Thermalization algorithms for classical gauge theories

abstract:
  I propose a method, based on a set of Langevin equations, for bringing
classical gauge theories to thermal equilibrium while respecting the set of
Gauss' constraints exactly. The algorithm is described in detail for the SU(2)
gauge theory with or without the Higgs doublet. As an example of application,
canonical average of the maximal Lyapunov exponent is computed for the SU(2)
Yang-Mills theory.


title:
Phase structure and confinement properties of noncompact gauge theories
  I

abstract:
  In the context of reviewing noncompact lattice gauge models at zero and
finite temperature we study in detail a contribution of the invariant measure
and the time-like plaquette configurations to correlation functions, analyze
the problem of the compactness of the potentials in respect to the confinement
and indicate the essential features to deal with the Wilson gauge theory in the
weak coupling region. A method for calculating an effective confining
noncompact model is also proposed.


title: A Study of Degenerate Four-quark states in SU(2) Lattice Monte Carlo

abstract:
  The energies of four-quark states are calculated for geometries in which the
quarks are situated on the corners of a series of tetrahedra and also for
geometries that correspond to gradually distorting these tetrahedra into a
plane. The interest in tetrahedra arises because they are composed of {\bf
three } degenerate partitions of the four quarks into two two-quark colour
singlets. This is an extension of earlier work showing that geometries with
{\bf two} degenerate partitions (e.g.\ squares) experience a large binding
energy. It is now found that even larger binding energies do not result, but
that for the tetrahedra the ground and first excited states become degenerate
in energy. The calculation is carried out using SU(2) for static quarks in the
quenched approximation with $\beta=2.4$ on a $16^3\times 32$ lattice. The
results are analysed using the correlation matrix between different euclidean
times and the implications of these results are discussed for a model based on
two-quark potentials.


title: Spin Models on Thin Graphs

abstract:
  We discuss the utility of analytical and numerical investigation of spin
models, in particular spin glasses, on ordinary ``thin'' random graphs (in
effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two
dimensional gravity. We highlight the similarity with Bethe lattice
calculations and the advantages of the thin graph approach both analytically
and numerically for investigating mean field results.


title: Polarized and Unpolarized Nucleon Structure Functions from Lattice QCD

abstract:
  We report on a high statistics quenched lattice QCD calculation of the
deep-inelastic structure functions $F_1$, $F_2$, $g_1$ and $g_2$ of the proton
and neutron. The theoretical basis for the calculation is the operator product
expansion. We consider the moments of the leading twist operators up to spin
four. Using Wilson fermions the calculation is done for three values of
$\kappa$, and we perform the extrapolation to the chiral limit. The
renormalization constants, which lead us from lattice to continuum operators,
are calculated in perturbation theory to one loop order.


title: Lattice energy sum rules and the trace anomaly

abstract:
  We show that the additional contribution to the Michael lattice energy sum
rule for the static quark-antiquark potential, pointed out recently, can be
identified with the contribution to the field energy arising from the trace
anomaly of the energy momentum tensor. We also exlicitely exhibit the anomalous
contribution to the field energy in the sum rule for the glueball mass obtained
recently by Michael.


title: Simplicial Quantum Gravity

abstract:
  This is my PhD thesis on four-dimensional simplicial quantum gravity using
the dynamical triangulation model. Most of the results we have published in
separate papers are collected here for your convenience. Some new results have
been added as well. Besides these results this thesis also contains an
introduction to simplicial quantum gravity and a detailed description of my
dynamical triangulation program for arbitrary dimension. Some small formal
parts are in Dutch.


title: Computation of Structure Functions From a Lattice Hamiltonian

abstract:
  We compute structure functions in the Hamiltonian formalism on a momentum
lattice using a physically motivated regularisation that links the maximal
parton number to the lattice size. We show for the $\phi ^4 _{3+1}$ theory that
our method allows to describe continuum physics. The critical line and the
renormalised mass spectrum close to the critical line are computed and scaling
behaviour is observed in good agreement with L{\"u}scher and Weisz' lattice
results. We then compute distribution functions and find a $Q^2$ behaviour and
the typical peak at $x_B\rightarrow 0$ like in $QCD$.


title:
Finite-Temperature Phase Structure of Lattice QCD with Wilson Quark
  Action

abstract:
  The long-standing issue of the nature of the critical line of lattice QCD
with the Wilson quark action at finite-temperatures, defined to be the line of
vanishing pion screening mass, and its relation to the line of
finite-temperature chiral tansition is examined. Analytical and numerical
evidence are presented that the critical line forms a cusp at a finite gauge
coupling, and the line of chiral transition runs past the tip of the cusp
without touching the critical line. Implications on the continuum limit and the
flavor dependence of chiral transition are discussed.


title:
SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane and Scaling
  Along the Wilson Axis

abstract:
  We present further evidence for the bulk nature of the phase transition line
in the fundamental--adjoint action plane of SU(3) lattice gauge theory.
Computing the string tension and some glueball masses along the thermal phase
transition line of finite temperature systems with $N_t=4$, which was found to
join onto the bulk transition line at its endpoint, we find that the ratio
$\sqrt{\sigma} / T_c$ remains approximately constant. However, the mass of the
$0^{++}$ glueball decreases as the endpoint of the bulk transition line is
approached, while the other glueball masses appear unchanged. This is
consistent with the notion that the bulk transition line ends in a critical
endpoint, with the continuum limit there being a $\phi^4$ theory with a
diverging correlation length only in the $0^{++}$ channel. We comment on the
implications for the scaling behavior along the fundamental or Wilson axis.


title: SO(3) vortices and disorder in the 2d SU(2) chiral model

abstract:
  We study the correlation function of the 2d SU(2) principal chiral model on
the lattice. By rewriting the model in terms of Z(2) degrees of freedom coupled
to SO(3) vortices we show that the vortices play a crucial role in disordering
the correlations at low temperature. Using a series of exact transformations we
prove that, if satisfied, certain inequalities between vortex correlations
imply exponential fall-off of the correlation function at arbitrarily low
temperatures. We also present some Monte Carlo evidence that these correlation
inequalities are indeed satisfied. Our method can be easily translated to the
language of 4d SU(2) gauge theory to establish the role of corresponding SO(3)
monopoles in maintaining confinement at small couplings.


title:
Character Expansion, Zeros of Partition Function and $\theta$-term in
  U(1) Gauge Theory

abstract:
  Character expansion developed in real space renormalization group (RSRG)
approach is applied to U(1) lattice gauge theory with $\th$-term in 2
dimensions. Topological charge distribution $P(Q)$ is shown to be of Gaussian
form at any $\b$(inverse coupling constant). The partition function $Z(\th)$ at
large volume is shown to be given by the elliptic theta function. It provides
the information of the zeros of partition function as an analytic function of
$\ze= e^{i \th}$ ($\th$ = theta parameter). These partition function zeros lead
to the phase transition at $\th=\pi$. Analytical results will be compared with
the MC simulation results. In MC simulation, we adopt (i)``set method" and
(ii)``trial function method".


title:
The running coupling from the QCD Schr\"odinger functional -- a one-loop
  analysis

abstract:
  Starting from the Schr\"odinger functional, we give a non-perturbative
definition of the running coupling constant in QCD. The spatial boundary
conditions for the quark fields are chosen such that the massless Dirac
operator in the classical background field has a large smallest eigenvalue. At
one-loop order of perturbation theory, we determine the matching coefficient to
the $\MSbar$-scheme and discuss the quark mass effects in the $\beta$-function.
To this order, we also compute the Symanzik improvement coefficient necessary
to remove the $\Oa$ lattice artefacts originating from the boundaries. For
reasonable lattice resolutions and the standard Wilson action, lattice
artefacts are found to be only weakly dependent on the lattice spacing $a$,
while they vanish quickly with the improved action of Sheikholeslami and
Wohlert.


title: Lattice Fermions without Doublers

abstract:
  By placing fermions only on the even sites of a lattice, one may halve the
momentum spectrum and construct a theory without doublers. The interaction is
nonlocal. The fermion propagator is not a sparse matrix, but because the
unwanted fermionic states are absent from the formalism, it is 256 times
smaller than the usual propagator.


title: Universality Class of $O(N)$ Models

abstract:
  We point out that existing numerical data on the correlation length and
magnetic susceptibility suggest that the two dimensional $O(3)$ model with
standard action has critical exponent $\eta=1/4$, which is inconsistent with
asymptotic freedom. This value of $\eta$ is also different from the one of the
Wess-Zumino-Novikov-Witten model that is supposed to correspond to the $O(3)$
model at $\theta=\pi$.


title: QCD Monopoles and Chiral Symmetry Breaking on SU(2) Lattices

abstract:
  Pseudoscalar correlator is measured in a singular (monopole dominant) and a
regular (photon dominant) parts of a maximal abelian field on SU(2) lattice. In
the abelian field and its singular part, light pseudoscalar boson are observed
similar to that in SU(2) field. On the other hand , the correlator in the
regular part behaves like a product of free quark and anti-quark. Obtained
results give a support for a possibility that monopole condensation is
responsible for chiral symmetry breaking as well as confinement. Correlation
between monopoles and instantons is also investigated by observing topological
charge. A field including monopoles carrys topological charge with good
correlation to that in original SU(2) gauge field while that including only
photons shows no topological charge.


title: The principle of indirect elimination

abstract:
  The principle of indirect elimination states that an algorithm for solving
discretized differential equations can be used to identify its own
bad-converging modes. When the number of bad-converging modes of the algorithm
is not too large, the modes thus identified can be used to strongly improve the
convergence. The method presented here is applicable to any standard algorithm
like Conjugate Gradient, relaxation or multigrid. An example from theoretical
physics, the Dirac equation in the presence of almost-zero modes arising from
instantons, is studied. Using the principle, bad-converging modes are removed
efficiently. Applied locally, the principle is one of the main ingredients of
the Iteratively Smooting Unigrid algorithm.


title:
Monopole Currents in U(1) Lattice Gauge Theory: A Comparison to an
  Effective Model based on Dual Superconductivity

abstract:
  We compare U(1) lattice gauge theory to an effective model of Maxwell and
London equations. In the effective model there is only one free parameter, the
London penetration depth lambda. It turns out that one can get good agreement
between both models if one modifies the usual definition of magnetic monopole
currents in U(1) lattice gauge theory. This comparison also shows that already
at small distances fluctuations of the occuring string are important. Further,
we investigate the beta-dependence of the penetration depth and determine the
suppression of the monopole condensate in flux tubes.


title:
Residual meson-meson interaction from lattice gauge simulation in a
  simple QED model

abstract:
  The residual interaction for a meson-meson system is computed utilizing the
cumulant, or cluster, expansion of the momentum-space time correlation matrix.
The cumulant expansion serves to define asymptotic, or free, meson-meson
operators. The definition of an effective interaction is then based on a
comparison of the full (interacting) and the free (noninteracting) time
correlation matrices. The proposed method, which may straightforwardly be
transcribed to other hadron-hadron systems, here is applied to a simple 2+1
dimensional U(1) lattice gauge model tuned such that it is confining. Fermions
are treated in the staggered scheme. The effective interaction exhibits a
repulsive core and attraction at intermediate relative distances. These
findings are consistent with an earlier study of the same model utilizing
L\"{u}scher's method where scattering phase shifts are obtained directly.


title: Marginally stable solutions

abstract:
  In previous work constant magnetic field strength solutions for SU(2) gauge
theory on a torus were found, which somewhat surprisingly turned out to be
classically stable. This was called marginal stability, as moving along one of
its zero-modes, two of the stable modes turn unstable. Here we investigate the
stability under quantum fluctuations in the domain where the solutions possess
the marginal stability at the classical level.


title:
Non-Perturbative Renormalisation of the Lattice $\Delta s=2$
  Four-Fermion Operator

abstract:
  We compute the renormalised four-fermion operator $O^{\Delta S=2}$ using a
non-perturbative method recently introduced for determining the renormalisation
constants of generic lattice composite operators. Because of the presence of
the Wilson term, $O^{\Delta S=2}$ mixes with operators of different
chiralities. A projection method to determine the mixing coefficients is
implemented. The numerical results for the renormalisation constants have been
obtained from a simulation performed using the SW-Clover quark action, on a
$16^3 \times 32$ lattice, at $\beta=6.0$. We show that the use of the constants
determined non-perturbatively improves the chiral behaviour of the lattice kaon
matrix element $\<\bar K^0| O^{\Delta S=2} | K^0\>_{\latt}$.


title:
Extraction of hadron-hadron potentials on the lattice within 2+1
  dimensional QED

abstract:
  A potential between mesons is extracted from 4-point functions within lattice
gauge theory taking 2+1 dimensional QED as an example. This theory possesses
confinement and dynamical fermions. The resulting meson-meson potential has a
short-ranged hard repulsive core due to antisymmetrization. The expected
dipole-dipole forces lead to attraction at intermediate distances. Sea quarks
lead to a softer form of the total potential.


title:
On the nature of the residual meson-meson interaction from simulations
  with a QED${}_{2+1}$ model

abstract:
  A potential between mesons is extracted from 4-point functions within lattice
gauge theory taking 2+1 dimensional QED as an example. This theory possesses
confinement and dynamical fermions. The resulting meson-meson potential has a
short-ranged hard repulsive core and the expected dipole-dipole forces lead to
attraction at intermediate distances. Sea quarks lead to a softer form of the
total potential.


title: Domain-wall fermions with $U(1)$ dynamical gauge fields

abstract:
  We have carried out a numerical simulation of a domain-wall model in
$(2+1)$-dimensions, in the presence of a dynamical gauge field only in an extra
dimension, corresponding to the weak coupling limit of a ( 2-dimensional )
physical gauge coupling. Using a quenched approximation we have investigated
this model at $\beta_{s} ( = 1 / g^{2}_{s} ) =$ 0.5 ( ``symmetric'' phase),
1.0, and 5.0 (``broken'' phase), where $g_s$ is the gauge coupling constant of
the extra dimension. We have found that there exists a critical value of a
domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero
mode on the domain-wall from the one without it, in both symmetric and broken
phases. This result suggests that the domain-wall method may work for the
construction of lattice chiral gauge theories.


title: Fixed point actions for SU(3) gauge theory

abstract:
  We summarize our recent work on the construction and properties of fixed
point (FP) actions for lattice $SU(3)$ pure gauge theory. These actions have
scale invariant instanton solutions and their spectrum is exact through
1--loop, i.e. in their physical predictions there are no $a^n$ nor $g^2 a^n$
cut--off effects for any $n$. We present a few-parameter approximation to a
classical FP action which is valid for short correlation lengths. We perform a
scaling test of the action by computing the quantity $G = L \sqrt{\sigma(L)}$,
where the string tension $\sigma(L)$ is measured from the torelon mass $\mu = L
\sigma(L)$, on lattices of fixed physical volume and varying lattice spacing
$a$. While the Wilson action shows scaling violations of about ten per cent,
the approximate fixed point action scales within the statistical errors for $
1/2 \ge aT_c$.


title: Topological Charge Distribution and $CP^1$ Model with $\theta$ Term

abstract:
  The two dimensional $CP^1$ model with $\theta$ term is simulated. We compute
the topological charge distribution $P(Q)$ by employing the ``set method" and
``trial function method", which are effective in the calculations for very wide
range of $Q$ and large volume. The distribution $P(Q)$ shows the Gaussian
behavior in the small $\beta$ (inverse coupling constant) region and deviates
from it in the large $\beta$ region. The free energy and its moment are
calculated as a function of $\theta$. For small $\beta$, the partition function
is given by the elliptic theta function, and the distribution of its zeros on
the complex $\theta$ plane leads to the first order phase transition at
$\theta=\pi$. In the large $\beta$ region, on the other hand, this first order
phase transition disappears, but definite conclusion concerning the transition
is not reached due to large errors.


title: Gonihedric 3D Ising Actions

abstract:
  We investigate a generalized Ising action containing nearest neighbour, next
to nearest neighbour and plaquette terms that has been suggested as a potential
string worldsheet discretization on cubic lattices by Savvidy and Wegner. We
use both mean field techniques and Monte-Carlo simulations to sketch out the
phase diagram.
  The Gonihedric (Savvidy-Wegner) model has a symmetry that allows any plane of
spins to be flipped with zero energy cost, which gives a highly degenerate
vacuum state. We choose boundary conditions in the simulations that eliminate
this degeneracy and allow the definition of a simple ferromagnetic order
parameter. This in turn allows us to extract the magnetic critical exponents of
the system.


title:
Exploring Correlation Methods to Determine QCD beta-Functions on the
  Lattice

abstract:
  We investigate -- as an alternative to usual Monte Carlo Renormalization
Group methods -- the feasibility of extracting QCD beta-functions directly from
a lattice analysis of correlations between the action and Wilson loops. We test
this correlation technique numerically in four dimensional SU(2) gauge theory,
on a 16^4 lattice at beta = 2.5 and find very promising results.


title:
Instantons and the fixed point topological charge in the two-dimensional
  O(3) sigma-model

abstract:
  We define a fixed point topological charge for the two-dimensional O(3)
lattice sigma-model which is free of topological defects. We use this operator
in combination with the fixed point action to measure the topological
susceptibility for a wide range of correlation lengths. The results strongly
suggest that it is not a physical quantity in this model. The procedure,
however, can be applied to other asymptotically free theories as well.


title: Xtoys: cellular automata on xwindows

abstract:
  Xtoys is a collection of xwindow programs for demonstrating simulations of
various statistical models. Included are xising, for the two dimensional Ising
model, xpotts, for the $q$-state Potts model, xautomalab, for a fairly general
class of totalistic cellular automata, xsand, for the Bak-Tang-Wiesenfield
model of self organized criticality, and xfires, a simple forest fire
simulation. The programs should compile on any machine supporting xwindows.


title:
Heavy Quark Spectroscopy and Matrix Elements: A Lattice Study using the
  Static Approximation

abstract:
  We present results of a lattice analysis of the $B$ parameter, $B_B$, the
decay constant $f_B$, and several mass splittings using the static
approximation. Results were obtained for 60 quenched gauge configurations
computed at $\beta=6.2$ on a lattice size of $24^3\times48$. Light quark
propagators were calculated using the $O(a)$-improved Sheikholeslami-Wohlert
action. We find $\Bbstat(m_b) = 0.69\er{3}{4} {\rm(stat)}\er{2}{1}
{\rm(syst)}$, corresponding to $\Bbstat = 1.02\er{5}{6}\er{3}{2}$, and $\fbstat
= 266\err{18}{20}\err{28}{27} \mev$, $f_{B_s}^2 B_{B_s}/f_B^2 B_B =
1.34\er{9}{8}\er{5}{3}$, where a variational fitting technique was used to
extract $\fbstat$. For the mass splittings we obtain $M_{B_s}-M_{B_d} =
87\err{15}{12}\err{6}{12} \mev$, $M_{\Lambda_b}-M_{B_d} =
420\errr{100}{90}\err{30}{30} \mev$ and $M_{B^*}^2-M_B^2 =
0.281\err{15}{16}\err{40}{37} \gev^2$. We compare different smearing techniques
intended to improve the signal/noise ratio. From a detailed assessment of
systematic effects we conclude that the main systematic uncertainties are
associated with the renormalisation constants relating a lattice matrix element
to its continuum counterpart. The dependence of our findings on lattice
artefacts is to be investigated in the future.


title:
The Hierarchical $\phi^4$ - Trajectory by Perturbation Theory in a
  Running Coupling and its Logarithm

abstract:
  We compute the hierarchical $\phi^4$-trajectory in terms of perturbation
theory in a running coupling. In the three dimensional case we resolve a
singularity due to resonance of power counting factors in terms of logarithms
of the running coupling. Numerical data is presented and the limits of validity
explored. We also compute moving eigenvalues and eigenvectors on the trajectory
as well as their fusion rules.


title: Unquenching the Schwinger Model (revised)

abstract:
  We study the quenched and unquenched lattice Schwinger model with Wilson
fermions. The lowest non-trivial order of the systematic expansion recently
proposed by Sexton and Weingarten is shown to allow good estimates of long
distance physics from quenched configurations. Results for the static potential
and the lowest bound state mass are presented.


title: Critical Behaviour of the Two Dimensional Step Model

abstract:
  We use finite--size scaling of Lee--Yang partition function zeroes to study
the critical behaviour of the two dimensional step or sgn $O(2)$ model. We
present evidence that, like the closely related $XY$--model, this has a phase
transition from a disordered high temperature phase to a low temperature
massless phase where the model remains critical. The critical parameters
(including logarithmic corrections) are compatible with those of the
$XY$--model indicating that both models belong to the same universality class.


title: Properties of the Z(3) Interface in (2+1)-D SU(3) Gauge Theory

abstract:
  A study is made of some properties of this interface in the SU(3) pure gauge
theory in 2+1 dimensions. At high temperatures, the interface tension is
measured and shows agreement with the perturbative prediction. Near the
critical temperature, the behaviour of the interface is examined, and its
fluctuations compared to a scalar field theory model.


title: High density QCD with static quarks

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


title:
Performance of the Cray T3D and Emerging Architectures on Canopy QCD
  Applications

abstract:
  The Cray T3D, an MIMD system with NUMA shared memory capabilities and in
principle very low communications latency, can support the Canopy framework for
grid-oriented applications. CANOPY has been ported to the T3D, with the intent
of making it available to a spectrum of users. The performance of the T3D
running Canopy has been benchmarked on five QCD applications extensively run on
ACPMAPS at Fermilab, requiring a variety of data access patterns. The net
performance and scaling behavior reveals an efficiency relative to peak Gflops
almost identical to that achieved on ACPMAPS. Detailed studies of the major
factors impacting performance are presented. Generalizations applying this
analysis to the newly emerging crop of commercial systems reveal where their
limitations will lie. On these applications, efficiencies of above 25\% are not
to be expected; eliminating overheads due to Canopy will improve matters, but
by less than a factor of two.


title: Baby Universes in 4d Dynamical Triangulation

abstract:
  We measure numerically the distribution of baby universes in the crumpled
phase of the dynamical triangulation model of 4d quantum gravity. The relevance
of the results to the issue of an exponential bound is discussed. The data are
consistent with the existence of such a bound.


title: Four-point renormalized coupling constant in O(N) models

abstract:
  The renormalized zero-momentum four-point coupling $g_r$ of $O(N)$-invariant
scalar field theories in $d$ dimensions is studied by applying the $1/N$
expansion and strong coupling analysis. The $O(1/N)$ correction to the
$\beta$-function and to the fixed point value $g_r^*$ are explictly computed.
Strong coupling series for lattice non-linear $\sigma$ models are analyzed near
criticality in $d=2$ and $d=3$ for several values of $N$ and the corresponding
values of $g_r^*$ are extracted. Large-$N$ and strong coupling results are
compared with each other, finding a good general agreement. For small $N$ the
strong coupling analysis in 2-d gives the best determination of $g^*_r$ to date
(or comparable for $N=2,3$ with the available Monte Carlo estimates), and in
3-d it is consistent with available $\phi^4$ field theory results.


title: RTNN: The new parallel machine in Zaragoza

abstract:
  I report on the development of RTNN, a parallel computer designed as a 4^4
hypercube of 256 T9000 transputer nodes, each with 8 MB memory. The peak
performance of the machine is expected to be 2.5 Gflops.


title: The SU(2) Confining Vacuum as a Dual Superconductor

abstract:
  We investigate the dual superconductivity hypothesis in pure SU(2) lattice
gauge theory. We find evidence of the dual Meissner effect both in the
maximally Abelian gauge and without gauge fixing. We also obtain a rather good
extimation of the string tension using the value of the London penetration
length.


title: On the phase structure of QCD with Wilson fermions

abstract:
  The phase structure of lattice QCD with Wilson fermions is discussed.
Analytic and numerical evidences are given for the spontaneous breaking of
parity and flavor symmetry, which naturally explains the existence of the
massless pion at the critical hopping parameter $K_c$ without recourse to the
chiral symmetry absent in the Wilson fermion formulation. New numerical
evidences are also presented for the multiple structure of the critical lines
in the weak coupling region. A connection between the phase structure and the
finite temperature phase transition is briefly mentioned.


title: Spin and Gauge Systems on Spherical Lattices

abstract:
  We present results for 2D and 4D systems on lattices with topology homotopic
to the surface of a (hyper) sphere $S^2$ or $S^4$. Finite size scaling is
studied in situations with phase transitions of first and second order type.
The Ising and Potts models exhibit the expected behaviour; for the 4D pure
gauge $U(1)$ theory we find consistent scaling indicative of a second order
phase transition with critical exponent $\nu\simeq 0.36(1)$.


title: More on SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane

abstract:
  We present further evidence for the bulk nature of the phase transition line
in the fundamental--adjoint action plane of SU(3) lattice gauge theory.
Computing the string tension and some glueball masses along the thermal phase
transition line of finite temperature systems with $N_t=4$, which was found to
join onto the bulk transition line at its endpoint, we find that the ratio
$\sqrt{\sigma} / T_c$ remains approximately constant. However, the mass of the
$0^{++}$ glueball decreases as the endpoint of the bulk transition line is
approached, while the other glueball masses appear unchanged. This is
consistent with the notion that the bulk transition line ends in a critical
endpoint with the continuum limit there being a $\phi^4$ theory with a
diverging correlation length only in the $0^{++}$ channel.


title: Generalized Hyper-Systolic Algorithm

abstract:
  We generalize the hyper-systolic algorithm proposed in [1] for abstract data
structures on massive parallel computers with $n_p$ processors. For a problem
of size $V$ the communication complexity of the hyper-systolic algorithm is
proportional to $\sqrt{n_p}V$, to be compared with $n_pV$ for the systolic
case. The implementation technique is explained in detail and the example of
the parallel matrix-matrix multiplication is tested on the Cray-T3D.


title:
Chronological Inversion Method for the Dirac Matrix in Hybrid Monte
  Carlo

abstract:
  In Hybrid Monte Carlo simulations for full QCD, the gauge fields evolve
smoothly as a function of Molecular Dynamics time. Here we investigate improved
methods of estimating the trial or starting solutions for the Dirac matrix
inversion as superpositions of a chronological sequence of solutions in the
recent past. By taking as the trial solution the vector which minimizes the
residual in the linear space spanned by the past solutions, the number of
conjugate gradient iterations per unit MD time is decreased by at least a
factor of 2. Extensions of this basic approach to precondition the conjugate
gradient iterations are also discussed.


title: Study of gauge (in)dependence of monopole dynamics

abstract:
  We investigated the gauge (in)dependence of the confinement mechanism due to
monopole condensation in SU(2) lattice QCD by various abelian projections. We
found (1) the string tension can be reproduced by monopoles alone also in
Polyakov gauge and (2) the behaviors of the Polyakov loop at the critical
temperature seem to be explained by the uniformity breaking of the monopole
currents in every gauge.


title: Monopoles in High Temperature Phase of SU(2) QCD

abstract:
  We investigated a behavior of monopole currents in the high temperature phase
of abelian projected finite temperature SU(2) QCD in maximally abelian gauge.
Wrapped monopole currents which are closed by periodic boundary play an
important role for the spatial string tension. And the wrapped monopole current
density seems to be non-vanishing in the continuum limit. These results may be
related to Polyakov's analysis of the confinement mechanism using monopole gas
in 3-dimensional SU(2) gauge theory with Higgs fields.


title: Block spin transformation on the dual lattice and monopole action

abstract:
  To find a perfect lattice action in terms of monopole action on the dual
lattice, we performed simulations of a monopole effective action obtained
numerically from vacuum configurations in SU(2) QCD. Although the Polyakov loop
behavior near $T_c$ is well reproduced by the action, a small but repulsive
term is needed in addition to get the string tension correctly. It is reported
also a monopole effective action in $SU(3)$ QCD which is expressed by one kind
of monopole currents.


title: Monopoles and hadron spectrum in quenched QCD

abstract:
  We report the preliminary results of the studies of hadron spectrum under the
background of abelian and monopole gauge fields in quenched Wilson SU(3) QCD.
Abelian gauge fields alone reproduce the same chiral limit as in the full case.
Critical hopping parameter $\kappa_c$ and $m_{\rho}$ are the same in both
cases. We need more time to get a definite result in the case of monopole
background. The photon contribution do not produce any mass gap in the chiral
limit ($\kappa=\kappa_c\sim 0.17$). The behavior is similar to those in the
free photon case for $\kappa_c= 0.125$.


title: B Physics with NRQCD: A Quenched Study

abstract:
  We present results on the spectrum of B mesons and heavy baryons, using a
non-relativistic formulation for the heavy and a clover action for the light
quark. We also discuss B meson decay constants and their dependency upon the
heavy meson mass.


title:
Status of the Finite Temperature Electroweak Phase Transition on the
  Lattice

abstract:
  I review the status of non-perturbative investigations of the finite
temperature electroweak phase transition by means of lattice simulations.


title: Glueball Spectroscopy on S^3

abstract:
  For SU(2) gauge theory on the three-sphere we implement the influence of the
boundary of the fundamental domain, and in particular the $\theta$-dependence,
on a subspace of low-energy modes of the gauge field. We construct a basis of
functions that respect these boundary conditions and use these in a variational
approximation of the spectrum of the lowest order effective hamiltonian.


title: 2-dimensional Regge gravity in the conformal gauge

abstract:
  By restricting the functional integration to the Regge geometries, we give
the discretized version of the well known path integral formulation of
2--dimensional quantum gravity in the conformal gauge. We analyze the role
played by diffeomorphisms in the Regge framework and we give an exact
expression for the Faddeev--Popov determinant related to a Regge surface; such
an expression in the smooth limit goes over to the correct continuum result.


title:
Continuum Limits and Exact Finite-Size-Scaling Functions for
  One-Dimensional $O(N)$-Invariant Spin Models

abstract:
  We solve exactly the general one-dimensional $O(N)$-invariant spin model
taking values in the sphere $S^{N-1}$, with nearest-neighbor interactions, in
finite volume with periodic boundary conditions, by an expansion in
hyperspherical harmonics. The possible continuum limits are discussed for a
general one-parameter family of interactions, and an infinite number of
universality classes is found. For these classes we compute the
finite-size-scaling functions and the leading corrections to finite-size
scaling. A special two-parameter family of interactions (which includes the
mixed isovector/isotensor model) is also treated, and no additional
universality classes appear. In the appendices we give new formulae for the
Clebsch-Gordan coefficients and 6--$j$ symbols of the $O(N)$ group, and some
new generalizations of the Poisson summation formula; these may be of
independent interest.


title: Scattering in the quenched approximation

abstract:
  We study, in the quenched approximation, Luescher's relation between pion
scattering lengths and the finite-volume energy of two pions at rest. The
quenched relation is drastically different from the full theory one; in
particular, ``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$
occur at one loop ($L$ is the linear size of the box), due to the special
properties of the $\eta'$ in the quenched approximation. Numerical examples
show that the size of these effects can be substantial.


title: Lattice Chiral Fermions

abstract:
  I review the ongoing attempts to define chiral gauge theories using the
lattice regularization.


title: Characterization of phases and boundary effects in U(1) gauge theory

abstract:
  We show that the two phases of the 4-dimensional compact U(1) lattice gauge
theory are characterized by the existence or absence of an infinite current
network, defining ``infinite'' on a finite lattice in a manner appropriate to
the chosen boundary conditions. In addition for open and fixed boundary
conditions we demonstrate the effects of inhomogeneities and provide examples
of the reappearance of an energy gap.


title: Strong-coupling expansion of lattice O(N) sigma models

abstract:
  We report progress in the computation and analysis of strong-coupling series
of two- and three-dimensional ${\rm O}(N)$ $\sigma$ models. We show that,
through a combination of long strong-coupling series and judicious choice of
observables, one can compute continuum quantities reliably and with a precision
at least comparable with the best available Monte Carlo data.


title: Running coupling constant and correlation length from Wilson loops

abstract:
  We consider a definition of the QCD running coupling constant $\alpha(\mu)$
related to Wilson loops of size $r{\times}t$ with arbitrary fixed $t/r$. The
schemes defined by these couplings are very close to the $\overline{\rm MS}$
scheme for all values of $t/r$; in the $t/r\to\infty$ limit, the ``$q\bar q$
force'' scheme is recovered. We propose a definition of correlation length,
also related to Wilson loops, which can be applied to the Monte Carlo
evaluation of $\alpha(\mu)$ up to very large momentum scales by use of
finite-size scaling techniques.


title: Why the overlap formula does not lead to chiral fermions

abstract:
  We describe a conceptually simple, but important test for the overlap
approach to the construction of lattice chiral gauge theories. We explain the
equivalence of the overlap formula with a certain waveguide model for a simple
set of gauge configurations (the trivial orbit). This equivalence is helpful in
carrying out the test, and casts serious doubts on the viability of the overlap
approach. A recent note by Narayanan and Neuberger which points out a mistake
in our previous work is irrelevant in this context.


title: Abelian Dominance of Chiral Symmetry Breaking in Lattice QCD

abstract:
  Calculations of the chiral condensate on the lattice using staggered fermions
and the Lanczos algorithm are presented. Four gauge fields are considered: the
quenched non-Abelian field, an Abelian projected field, and monopole and photon
fields further decomposed from the Abelian field. Abelian projection is
performed in maximal Abelian gauge and in Polyakov gauge. The results show that
monopoles in maximal Abelian gauge largely reproduce the chiral condensate
values of the full non-Abelian theory, in both SU(2) and SU(3) color.


title:
Chiral behaviour of the lattice $B_K$-parameter with the Wilson and
  Clover Actions at $\beta = 6.0$

abstract:
  We present results for the kaon $B$-parameter $B_K$ from a sample of $200$
configurations using the Wilson action and $460$ configurations using the
SW-Clover action, on a $18^3 \times 64$ lattice at $\beta=6.0$. We compare
results obtained by renormalizing the relevant operator with different
``boosted" values of the strong coupling constant $\alpha_s$. In the case of
the SW-Clover action, we also use the operator renormalized non-perturbatively.
In the Wilson case, we observe a strong dependence of $B_K$ on the prescription
adopted for $\alpha_s$, contrary to the results of the Clover case which are
almost unaffected by the choice of the coupling. We also find that the matrix
element of the operator renormalized non-perturbatively has a better chiral
behaviour. This gives us our best estimate of the renormalization group
invariant $B$-parameter, $\hat B_K=0.86 \pm 0.15$.


title:
Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional
  Nonlinear $\sigma$-Models

abstract:
  We introduce a new and very convenient approach to multi-grid Monte Carlo
(MGMC) algorithms for general nonlinear $\sigma$-models: it is based on
embedding an $XY$ model into the given $\sigma$-model, and then updating the
induced $XY$ model using a standard $XY$-model MGMC code. We study the dynamic
critical behavior of this algorithm for the two-dimensional $O(N)$
$\sigma$-models with $N = 3,4,8$ and for the $SU(3)$ principal chiral model. We
find that the dynamic critical exponent $z$ varies systematically between these
different asymptotically free models: it is approximately 0.70 for $O(3)$, 0.60
for $O(4)$, 0.50 for $O(8)$, and 0.45 for $SU(3)$. It goes without saying that
we have no theoretical explanation of this behavior.


title:
Dynamic Critical Behavio(u)r of a Cluster Algorithm for the
  Ashkin--Teller Model

abstract:
  We study the dynamic critical behavior of a Swendsen--Wang--type algorithm
for the Ashkin--Teller model. We find that the Li--Sokal bound on the
autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$)
holds along the self-dual curve of the symmetric Ashkin--Teller model, but this
bound is apparently not sharp. The ratio $\tau_{{\rm int},{\cal E}}/C_H$
appears to tend to infinity either as a logarithm or as a small power ($0.05
\ltapprox p \ltapprox 0.12$).


title: Monte Carlo Methods for the Self-Avoiding Walk

abstract:
  This article is a pedagogical review of Monte Carlo methods for the
self-avoiding walk, with emphasis on the extraordinarily efficient algorithms
developed over the past decade. Many more details can be found in
hep-lat/9405016.


title:
Comparison between Theoretical Four-Loop Predictions and Monte Carlo
  Calculations in the Two-Dimensional $N$-Vector Model for $N=3,4,8$

abstract:
  We have computed the four-loop contribution to the beta-function and to the
anomalous dimension of the field for the two-dimensional lattice $N$-vector
model. This allows the determination of the second perturbative correction to
various long-distance quantities like the correlation lengths and the
susceptibilities. We compare these predictions with new Monte Carlo data for $N
= 3,4,8$. From these data we also extract the values of various universal
nonperturbative constants, which we compare with the predictions of the $1/N$
expansion.


title:
Application of the $O(N)$-Hyperspherical Harmonics to the Study of the
  Continuum Limits of One-Dimensional $\sigma$-Models and to the Generation of
  High-Temperature Expansions in Higher Dimensions

abstract:
  In this talk we present the exact solution of the most general
one-dimensional $O(N)$-invariant spin model taking values in the sphere
$S^{N-1}$, with nearest-neighbour interactions, and we discuss the possible
continuum limits. All these results are obtained using a high-temperature
expansion in terms of hyperspherical harmonics. Applications in higher
dimensions of the same technique are then discussed.


title: Improving the topological charge density operator on the lattice

abstract:
  We analyze the properties of a class of improved lattice topological charge
density operators, constructed by a smearing-like procedure. By optimizing the
choice of the parameters introduced in their definition, we find operators
having (i) a much better statistical behavior as estimators of the topological
charge density on the lattice, i.e. much less noisy; (ii) a multiplicative
renormalization much closer to one; (iii) a large suppression of the
perturbative tail in the corresponding lattice topological susceptibility.


title: Topological aspects of QCD

abstract:
  We review recent results from lattice on topological aspects of QCD: most of
the results refer to monopoles and to instantons. We discuss in detail the
evidence for condensation of monopoles in the vacuum and confinement of colour
by dual superconductivity, and the major role of monopoles in dynamics
(monopole dominance). As for instantons we review the $U(1)$ problem, a
possible determination of the spin content of the proton, and new lattice data
relevant to instanton liquid models.


title:
Chiral condensate, susceptibilities, critical coupling and indices in
  QED$_4$

abstract:
  We measure chiral susceptibilities in the Coulomb phase of noncompact QED$_4$
in $8^4, 10^4$ and $12^4$ lattices. The MFA approach allows simulations in the
chiral limit which are therefore free from arbitrary mass extrapolations. Using
the critical couplings extracted from these calculations, we study the critical
behaviour of the chiral condensate, which we find in disagreement with the
predictions of logarithmically improved scalar Mean Field theory.


title:
Tricritical point in strongly coupled U(1) gauge theory with fermions
  and scalars

abstract:
  We investigate the tricritical point in the lattice fermion--gauge--scalar
model with U(1) gauge symmetry. In the vicinity of this point, in the phase
with the broken chiral symmetry, we observe the scaling behavior of the chiral
condensate and of the masses of composite fermion and composite scalar,
indicating the existence of an interesting continuum limit of the model at this
point.


title: Critical Behavior of the Schwinger Model with Wilson Fermions

abstract:
  We present a detailed analysis, in the framework of the MFA approach, of the
critical behaviour of the lattice Schwinger model with Wilson fermions on
lattices up to $24^2$, through the study of the Lee-Yang zeros and the specific
heat. We find compelling evidence for a critical line ending at $\kappa = 0.25$
at large $\beta$. Finite size scaling analysis on lattices $8^2,12^2,16^2,
20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation
is verified in the explored $\beta$ region.


title: Magnetic and chiral universality classes in a 3D Yukawa model

abstract:
  The 3D Yukawa model with U(1) chiral symmetry is investigated in a broad
interval of parameters using the Binder method. Critical exponents of the
Wilson-Fisher (magnetic) and Gross-Neveu (chiral) universality classes are
measured. The model is dominated by the chiral universality class. However at
weak coupling we observe a crossover between both classes, manifested by
difficulties with the Binder method which otherwise works well.


title: Light hadron masses with 4-GeV cutoff and L=2.4fm

abstract:
  We discuss preliminary results from our quenched light hadron mass
calculation on a $48^3 \times 64$ lattice at the coupling of $\beta = 6.5$.
Staggered quarks with masses of $m_q = 0.01, 0.005, 0.0025$ and $0.00125$ are
used.


title: Gauge invariant generalization of the 2D chiral Gross-Neveu model

abstract:
  By means of the Lee-Shrock transformation we generalize the 2D Gross-Neveu
(GN$_2$) model to a U(1) gauge theory with charged fermion and scalar fields in
2D ($\chi U \phi_2$ model). The $\chi U \phi_2$ model is equivalent to the
GN$_2$ model at infinite gauge coupling. We show that the dynamical fermion
mass generation and asymptotic freedom in the effective four-fermion coupling
persist also when the gauge coupling decreases. These phenomena are not
influenced by the XY$_2$ model phase transition at weak coupling. This suggests
that the $\chi U \phi_2$ model is in the same universality class as the GN$_2$
model and thus renormalizable.


title: Tuning the generalized Hybrid Monte Carlo algorithm

abstract:
  We discuss the analytic computation of autocorrelation functions for the
generalized Hybrid Monte Carlo algorithm applied to free field theory and
compare the results with numerical results for the $O(4)$ spin model in two
dimensions. We explain how the dynamical critical exponent $z$ for some
operators may be reduced from two to one by tuning the amount of randomness
introduced by the updating procedure, and why critical slowing down is not a
problem for other operators.


title:
Quenched $SU(3)$ hadron spectroscopy using improved fermionic and gauge
  actions

abstract:
  We present results of quenched $SU(3)$ hadron spectroscopy using $\order(a)$
improved Wilson fermions. The configurations were generated using an
$\order(a^2)$ improved 6-link $SU(3)$ pure gauge action at $\beta$'s
corresponding to lattice spacings of $0.43$, $0.25$, $0.20$, $0.18$, and $0.15$
fm. We find evidence that fermionic scaling violations are consistent with
$\order(a^2)$ errors.


title: $f_B$ quenched and unquenched

abstract:
  Results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$, and their ratios are
presented. High statistics quenched runs at $\beta=5.7$, $5.85$, $6.0$, and
$6.3$, plus a run still in progress at $\beta=6.52$ make possible a preliminary
extrapolation to the continuum. The data allows good control of all systematic
errors except for quenching, although not all of the error estimates have been
finalized. Results from configurations which include effects of dynamical
quarks show a significant deviation from the quenched results and make possible
a crude estimate of the quenching error.


title: Some Applications of the Overlap Formalism

abstract:
  The massless vector Schwinger model with $N_f=1,2,3,4$ number of flavors is
studied on the lattice using the overlap formalism. A full Monte Carlo
simulation yields values for the bilinear fermion condensate that are in
agreement with the exact solution of the continuum Schwinger model with an
added Thirring interaction.


title: Progress in lattice chiral gauge theories

abstract:
  Some key features of continuum chiral fermions are shown to be satisfied by
the overlap.


title: Gauge invariant investigation of the nature of Confinement

abstract:
  We observe a strong correlation between the decrease in the number of action
density peaks in SU(2) Yang-Mills configurations with cooling and that of the
string tension. The nature and distribution of these peaks is investigated. The
relationship with monopole currents after the abelian projection is also
considered.


title:
Mass splittings and matrix elements of mesons and baryons containing a
  single heavy quark

abstract:
  We present a study in the quenched approximation of the $B$ parameter $B_B$
and the decay constant $f_B$ using heavy-quark propagators implemented in the
static approximation, and light-quark propagators computed using an
$O(a)$-improved fermion action. We find a value of $\Bbstat$ close unity, and
discuss the systematic errors entering into the calculation. $\fbstat$ is
extracted using a variational fitting technique in order to obtain a reliable
estimate of the ground state.
  In the second part of the talk, we describe an exploratory study of baryons
containing a single heavy quark, computed using the $O(a)$-improved fermion
action. We obtain masses generally in good agreement with experiment in both
the charm and beauty sectors. We also report preliminary results for the form
factor $G_1$ in the semi-leptonic $\Lambda_b \rightarrow \Lambda_c$ transition.


title: Coupling the Deconfining and Chiral Transitions

abstract:
  The Polyakov loop and the chiral condensate are used as order parameters to
explore analytically the possible phase structure of finite temperature QCD.
Nambu-Jona-Lasinio models in a background temporal gauge field are combined
with a Polyakov loop potential in a form suitable for both the lattice and the
continuum. Three possible behaviors are found: a first-order transition, a
second-order transition, and a region with both transitions.


title:
New results on $\gamma_{\rm str}$ in 2D quantum gravity using Regge
  calculus

abstract:
  We study 2D quantum gravity on spherical topologies using the Regge calculus
approach. Our goal is to shed new light upon the validity of the Regge approach
to quantum gravity, which has recently been questioned in the literature. We
incorporate an $R^2$ interaction term and investigate its effect on the value
of the string susceptibility exponent $\gamma_{\rm str}$ using two different
finite-size scaling Ans\"atze. Our results suggest severe shortcomings of the
methods used so far to determine $\GS$ and show a possible cure of the
problems. To have better control over the influence of irregular vertices, we
choose besides the almost regular triangulation of the sphere as the surface of
a cube a random triangulation according to the Voronoi-Delaunay prescription.


title: Perfect Lattice Actions with and without Chiral Symmetry

abstract:
  We use perturbation theory to construct perfect lattice actions for fermions
and gauge fields by blocking directly from the continuum. When one uses a
renormalization group transformation that preserves chiral symmetry the
resulting lattice action for massless fermions is chirally symmetric but
nonlocal. When the renormalization group transformation breaks chiral symmetry,
the lattice action becomes local but chiral symmetry is explicitly broken. In
particular, starting with a chiral gauge theory in the continuum one either
obtains a lattice theory which is gauge invariant but nonlocal, or a local
theory with explicitly broken gauge invariance. In both cases the spectrum of
the lattice theory is identical with the one of the continuum and the anomaly
is correctly reproduced. We also apply our techniques to vector-like theories.
In particular we propose a new renormalization group transformation for QCD and
we optimize its parameters for locality of the perfect action.


title:
Testing Haldane's Conjecture in the O(3) Model by a Meron Cluster
  Simulation

abstract:
  Twelve years ago, Haldane formulated his famous conjecture for 1-d
antiferromagnetic quantum spin chains. In the context of the 2-d O(3) model
with a \theta term, it predicts a phase transition at \theta = \pi, which has
not yet been verified reliably. To simulate this we use the Wolff cluster
algorithm together with an improved estimator for the topological charge
distribution. Each cluster carries integer or half integer charge. Clusters
with charge 1/2 are identified with merons. At \theta = \pi they are inactive,
such that the mass gap vanishes. We obtain critical exponents which are
consistent with predictions from the k=1 WZNW model, therefore confirming a
second order phase transition.


title: Complex-Temperature Singularities of Ising Models

abstract:
  We report new results on complex-temperature properties of Ising models.
These include studies of the $s=1/2$ model on triangular, honeycomb, kagom\'e,
$3 \cdot 12^2$, and $4 \cdot 8^2$ lattices. We elucidate the complex--$T$ phase
diagrams of the higher-spin 2D Ising models, using calculations of partition
function zeros. Finally, we investigate the 2D Ising model in an external
magnetic field, mapping the complex--$T$ phase diagram and exploring various
singularities therein. For the case $\beta H=i\pi/2$, we give exact results on
the phase diagram and obtain susceptibility exponents $\gamma'$ at various
singularities from low-temperature series analyses.


title: Two-flavor staggered-fermion thermodynamics at $N_t = 12$

abstract:
  We present new results in an ongoing study of the nature of the high
temperature crossover in QCD with two light fermion flavors. These results are
obtained with the conventional staggered fermion action at the smallest lattice
spacing to date---approximately 0.1 fm. Of particular interest are a study of
the temperature of the crossover, an important indicator of continuum scaling,
a determination of the induced baryon charge and baryon susceptibility, used to
study the dissolution of hadrons at the crossover, the scalar susceptibility, a
signal for the appearance of soft modes, and the chiral order parameter, used
to test models of critical behavior.


title:
2D Potts Model Correlation Lengths: Numerical Evidence for $\xi_o =
  \xi_d$ at $\beta_t$

abstract:
  We have studied spin-spin correlation functions in the ordered phase of the
two-dimensional $q$-state Potts model with $q=10$, 15, and 20 at the
first-order transition point $\beta_t$. Through extensive Monte Carlo
simulations we obtain strong numerical evidence that the correlation length in
the ordered phase agrees with the exactly known and recently numerically
confirmed correlation length in the disordered phase: $\xi_o(\beta_t) =
\xi_d(\beta_t)$. As a byproduct we find the energy moments in the ordered phase
at $\beta_t$ in very good agreement with a recent large $q$-expansion.


title: Correlation Length From Cluster-Diameter Distribution

abstract:
  We report numerical estimates of correlation lengths in 2D Potts models from
the asymptotic decay of the cluster-diameter distribution. Using this
observable we are able to verify theoretical predictions for the correlation
length in the disordered phase at the transition point for $q=10$, 15, and 20
with an accuracy of about $1%-2%$. This is a considerable improvement over
previous measurements using the standard (projected) two-point function.


title: Light hadron spectroscopy

abstract:
  I review the progress that has been made in light hadron spectroscopy from
lattice QCD, since the LATTICE'94 conference in Bielefeld.


title:
Scattering phases for fermion-fermion scattering in the Gross-Neveu
  model

abstract:
  We extract scattering phases for fermion-fermion scattering from Monte Carlo
simulations of the two-dimensional Gross-Neveu model. This is done by means of
L\"uscher's method, which exploits the volume dependence of the energies of
two-particle states. The results are compared with the analytical predictions.


title: $B$ Meson Matrix Elements from Various Heavy Quark Effective Theories

abstract:
  Various properties of heavy-light mesons are determined, including decay
constants, the $B_{B}$-parameter, and the Isgur-Wise function. The heavy
(bottom) quark is simulated with the static, NRQCD and/or (fixed-velocity)
lattice-HQET effective theories, using optimally-smeared sources as produced by
the ``Maximal Operator Smearing Technique''.


title: Delta-rho in an SU(2) X U(1) chiral Yukawa model

abstract:
  We report on a simulation in progress of an SU(2) X U(1) fermion-Higgs model
with two *non-degenerate* fermion doublets. The Zaragoza proposal for chiral
lattice fermions is used; naive fermions are studied for comparison. The aims
of this simulation are a non-perturbative study of the decoupling of species
doublers, of triviality bounds on the Higgs and fermion masses and of the
phenomenological quantity Delta-rho.


title: Determination of the Crumpling Fractal Dimension Via k-Space MCRG

abstract:
  Motivated by the successful application of MCRG in momentum space to $\lambda
\phi^4_3$ we determine the critical exponents at the crumpling transition in
fixed triangulated surfaces. The results are still tentative, but suggest that
$-1.0\ge \eta \ge -1.3$, pointing at a value for the fractal Hausdorff
dimension at the crumpling transistion fixed point somewhere between 3 and 4.


title: Hubbard Model with Luscher fermions - a progress report

abstract:
  Some modifications of the Luscher algorithm, which reduce the autocorelation
time, are proposed and tested.


title: Improved cooling algorithm for gauge theories

abstract:
  We propose and study a ``gold-washing" - type of algorithm which smooths out
the short range fluctuations but leaves invariant instantons above a certain
size. The algorithm needs no monitoring or calibration.


title:
Heavy-light meson decay constants from NRQCD: an analysis of the 1/M
  corrections

abstract:
  We present {\it preliminary} results for the decay constants of heavy-light
mesons using NRQCD heavy and tadpole improved Clover light quarks. A comparison
is made with data obtained using Wilson light quarks. We present an analysis of
the 1/M corrections to the decay constants in the static limit and compare with
the predictions of HQET.


title: Monte Carlo Study of 8-State Potts Model on 2D Random Lattices

abstract:
  We study the effect of quenched coordination-number disorder of random
lattices on the nature of the phase transition in the two-dimensional
eight-state Potts model, which is of first order on regular lattices. We
consider Poissonian random lattices of toroidal topology constructed according
to the Voronoi/Delaunay prescription. Monte Carlo simulations yield strong
evidence that the phase transition remains first order.


title: The Renormalized Trajectory of the O(N) Non-linear Sigma Model

abstract:
  The renormalized trajectory (RT) is determined from two different Monte Carlo
renormalization group techniques with $\delta$-function block spin
transformation in the multi-dimensional coupling parameter space of the
two-dimensional non-linear sigma model with O(3) symmetry. At a correlation
length $\xi \approx 3$-$5$, the RT is shown to break away from the straight
line of the fixed point trajectory (FPT) which is orthogonal to the critical
surface and originates from the ultraviolet fixed point (UVFP). The large $N$
calculation of the RT is also presented in the coupling parameter space of the
most general bilinear Hamiltonian. The RT in the large $N$ approximation
exhibits a similar shape with the sharp break occurring at a somewhat smaller
correlation length.


title: A study of the quark-gluon vertex

abstract:
  We present the first results from a study of the quark--gluon vertex function
in the Landau gauge. The results are obtained for quenched QCD with an
O(a)-improved Wilson fermion action, at beta=6.0. We discuss plans for further
study, including extraction of a renormalised QCD coupling from the momentum
dependence of the vertex.


title: The scalar glueball from a tadpole-improved action

abstract:
  The scalar glueball mass and the string tension are computed in lattice SU(3)
gauge theory with the aim of establishing the effectiveness of the improved
action approach in removing finite-spacing artifacts.


title: New results from mixed-action lattice gauge theory

abstract:
  We extend and attempt to clarify recent results which showed possible
problems for universality for the gauge group SU(2). We suggest that the
presence of artifacts actually distorts the mixed-coupling plane. This implies
that a separation of artifacts from physical quantities is intrinsically
difficult. We suggest what the nature of the resolution might be. Full results
will appear elsewhere.


title: Study of Cullum's and Willoughby's Lanczos method for Wilson fermions

abstract:
  The Lanczos method of Cullum and Willoughby is studied for euclidean Wilson
fermions in quenched and unquenched SU(2) gauge fields on lattices of volume
ranging from $4^4$ to $16^4$. The method is reliable even on larger lattices,
but its cost for the computation of a given fraction of the spectrum grows
(approximately) with the square of the lattice volume. We investigate the
convergence behaviour and show that it is closely linked with the local
spectral density. Complete spectra are determined on lattices up to $8^3 \cdot
12$. For configurations where all eigenvalues are computed, we give numerical
values for the fermionic determinants and results for spectral densities.
Determinants are also given for staggered fermions whose quenched and
unquenched spectra were studied in a previous publication.


title: Electromagnetic Self-Duality in a Lattice Model

abstract:
  We formulate a Euclidean lattice theory of interacting elementary spin-half
electric and magnetic charges, which we refer to as electrons and magnetic
monopoles respectively. The model uses the polymer representation of the
fermion determinant, and exhibits a self-dual symmetry provided electric charge
$e$ and magnetic charge $g$ obey the minimal Dirac quantisation condition
$eg=2\pi$. In a hopping parameter expansion at lowest order, we show that
virtual electron and monopole loops contribute radiative corrections of
opposite sign to the photon propagator. We argue that in the limit $e\to0$,
fermion mass $\mu\to0$, the model describes QED together with strongly
interacting monopoles whose chiral symmetry is spontaneously broken. Prospects
for the existence of an interacting continuum limit at the self-dual point
$e=g$ are discussed.


title: Lattice Perturbation Theory

abstract:
  Sources of uncertainties in perturbative calculations, tadpole improvement
and its role in lattice perturbation theory, and six recent calculations are
discussed.


title: The Phase Diagram of Crystalline Surfaces

abstract:
  We report the status of a high-statistics Monte Carlo simulation of
non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of
size up to $128^2$ nodes. We impose free boundary conditions. The free energy
is a gaussian spring tethering potential together with a normal-normal bending
energy. Particular emphasis is given to the behavior of the model in the cold
phase where we measure the decay of the normal-normal correlation function.


title: Status of the 0.8 Teraflops Supercomputer at Columbia

abstract:
  The first stage in the construction of the 0.8 Teraflops Supercomputer at
Columbia, a working, two node parallel computer, has been successfully
completed. The next stage, a 512 node, 26 Gigaflops prototype, is in its final
construction phase. A general description and current status of the hardware
and software is presented.


title: The continuum limit in the quenched approximation

abstract:
  Previous work at $6/g^2=5.7$ with quenched staggered quarks is extended with
new calculations at 5.85 and 6.15 on lattices up to $32^3\times 64$. These
calculations allow a more detailed study of extrapolation in quark mass, finite
volume and lattice spacing than has heretofore been possible. We discuss how
closely the quenched spectrum approaches that of the real world.


title: Monte Carlo studies of antiferromagnetic spin models in three dimensions

abstract:
  We study several antiferromagnetic formulations of the O(3) spin model in
three dimensions by means of Monte Carlo simulations. We discuss about the
vacua properties and analyze the phase transitions. Using Finite Size Scaling
analysis we conclude that all phase transitions found are of first order


title:
Non-perturbative renormalization of the $\Delta S=2$ operator and the
  heavy-light axial current

abstract:
  We apply a recently introduced non-perturbative renormalization method to two
types of lattice operators: the $\Delta S=2$ four fermion operator and the
heavy-light static axial current, which are relevant for the physics of $K$ and
$B$ mesons respectively. The results of the non-perturbative calculations of
the renormalization constants are compared with the corresponding perturbative
ones.


title:
A Lattice Evaluation of the Deep-Inelastic Structure Functions of the
  Nucleon

abstract:
  The lower moments of the unpolarized and polarized deep-inelastic structure
functions of the nucleon are calculated on the lattice. The calculation is done
with Wilson fermions and for three values of the hopping parameter $\kappa$, so
that we can perform the extrapolation to the chiral limit. Particular emphasis
is put on the renormalization of lattice operators. The renormalization
constants, which lead us from lattice to continuum operators, are computed
perturbatively to one loop order as well as non-perturbatively.


title: Variants of L\"uscher's fermion algorithm

abstract:
  We study improved variants of L\"uscher's algorithm, including the cases of
staggered fermions and finite density.


title:
Topological susceptibility and Instanton size distribution from
  over-improved cooling

abstract:
  We measure the topological susceptibility by cooling with an over-improved
action. In contrast with usual cooling, large instantons survive over-improved
cooling {\em indefinitely}. By varying the parameter of the over-improved
cooling action, we measure the instanton size distribution.


title: Progress on lattice QCD algorithms

abstract:
  I review recent progress on algorithms for calculating quark propagators and
for simulating full QCD.


title:
Masses and decay constants of the light mesons in the quenched
  approximation using the tadpole--improved SW-clover action

abstract:
  We present results for the masses and decay constants of the light mesons in
quenched QCD using the standard gluon action and a tadpole--improved SW--clover
fermionic action to reduce discretisation errors. The calculation has been
carried out at fixed volume and three lattice spacings corresponding to
$\beta=5.7$, $6.0$ and $6.2$. We make comparisons with the conventional
SW--clover scheme. We use our results to extract continuum limits and to
quantify the size of discretisation errors at smaller $\beta$-values.


title: Leptonic Decays of Heavy-Light Systems

abstract:
  Results from recent lattice calculations of the decay constants $f_B$ and
$f_D$ are reviewed. A discussion of the methods currently used is presented,
together with an outline of the various systematic effects involved.


title: Renormalons

abstract:
  The calculation of higher twist (or dimension) corrections to physical
quantities using operator product expansions is delicate. If dimensional
regularization is used to regulate the ultra-violet divergences then there are
ambiguities in the Wilson coefficient functions due to infra-red renormalon
singularities. With a hard ultra violet cut-off, such as the inverse lattice
spacing $a$, there are no renormalon ambiguities, as a result of cancellations
between terms which in finite orders of perturbation theory diverge as inverse
powers of $a$, and those which diverge at most logarithmically. In this lecture
I review these questions, explaining the steps necessary to obtain predictions
for physical quantities from lattice measurements of matrix elements of higher
dimensional operators. The ideas are illustrated by considering quantities
computed using the heavy quark effective theory beyond leading order in the
heavy quark mass.


title: Results from 3D Electroweak Phase Transition Simulations

abstract:
  We study the phase transition in SU(2)-Higgs model on the lattice using the
3D dimensionally reduced formalism. The 3D formalism enables us to obtain
highly accurate Monte Carlo results, which we extrapolate both to the infinite
volume and to the continuum limit. Our formalism also provides for a
well-determined and unique way to relate the results to the perturbation
theory. We measure the critical temperature, latent heat and interface tension
for Higgs masses up to 70 GeV.


title: The D234 action for light quarks

abstract:
  We investigate a new light fermion action (the ``D234'' action), which is
accurate up to $\O(a^3)$ and tadpole-improved $\O(a \alpha_s)$ errors. Using
D234 with Symanzik- and tadpole-improved glue we find evidence that continuum
results for the quenched hadron spectrum (pion, rho and nucleon) can be
obtained on coarse lattices.


title: Resonance Scattering on the Lattice with Non-Zero Total Momentum

abstract:
  Most hadronic particles are resonances: for example, the rho meson appears as
a resonance in the elastic scattering of two pions. A method by Luescher
enables one to measure the properties of the resonance particles from finite
lattices. We present here a more general method which includes scattering
processes where the total momentum of the particles is non-zero. The main
advantage is that the resonance scattering can be observed in a considerably
smaller spatial volume. We test the method with a simple 3+1 dimensional spin
model, and find excellent agreement between the zero momentum and the non-zero
momentum scattering sectors.


title: Surface modes and parity violation in Schwinger model on the lattice

abstract:
  The phase diagram of the Schwinger model on the lattice with Wilson fermions
is investigated in the Hartree-Fock approximation. In case of single flavour
(not directly amenable to simulations), the calculation indicates the existence
of the parity violating phase at both weak and intermediate-to-strong
couplings. Hartree-Fock vacuum sustains a nonzero electric field in this broken
phase. The phase structure of the model with two flavours is also discussed.


title: Hadronic Physics from the Lattice

abstract:
  We present the lattice gauge theory approach to evaluating non-perturbative
hadronic interactions from first principles. We discuss applications to
glueballs, inter-quark potentials, the running coupling constant, the light
hadron spectrum and the pseudoscalar decay constant $f_P$.


title:
Critical behaviour of SU(2) lattice gauge theory. A complete analysis
  with the $\chi^2$-method

abstract:
  We determine the critical point and the ratios $\beta/\nu$ and $\gamma/\nu$
of critical exponents of the deconfinement transition in $SU(2)$ gauge theory
by applying the $\chi^2$-method to Monte Carlo data of the modulus and the
square of the Polyakov loop. With the same technique we find from the Binder
cumulant $g_r$ its universal value at the critical point in the thermodynamical
limit to $-1.403(16)$ and for the next-to-leading exponent $\omega=1\pm0.1$.
From the derivatives of the Polyakov loop dependent quantities we estimate then
$1/\nu$. The result from the derivative of $g_r$ is $1/\nu=0.63\pm0.01$, in
complete agreement with that of the $3d$ Ising model.


title: On the U(2) Lattice Gauge Theory

abstract:
  We study the U(2) lattice gauge theory in the pure gauge sector using the
simplest action, with determinant and fundamental terms, having the naive
continuum limit of SU(2)$\times$U(1). We determine part of the phase diagram of
the model and find a first-order critical line which goes through the U(1)
critical point. We show how to deduce both the order parameter of the
first-order transition and the U(2) renormalization group flow from the lattice
potential in the determinant and fundamental representations. We give evidence
that a Monte-Carlo simulation of the model is indeed consistent with the
symmetric SU(2)$\times$U(1) continuum limit in the weak coupling pertubative
regime.


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

abstract:
  We improve the calculation of the equation of state for two flavor QCD by
simulating on $N_t=6$ lattices at appropriate values of the couplings for the
deconfinement/chiral symmetry restoration crossover. For $am_q=0.0125$ the
energy density rises rapidly to approximately 1 ${\rm GeV/fm^3}$ just after the
crossover($m_\pi/m_\rho\approx 0.4$ at this point). Comparing with our previous
result for $N_t=4$~\cite{eos}, we find large finite $N_t$ corrections as
expected from free field theory on finite lattices. We also provide formulae
for extracting the speed of sound from the measured quantities.


title:
Smooth interpolation of lattice gauge fields by signal processing
  methods

abstract:
  We digitally filter the Fourier modes of the link angles of an abelian
lattice gauge field which produces the Fourier modes of a continuum $A_\mu(x)$
that exactly reproduces the lattice links through their definition as phases of
finite parallel transport. The constructed interpolation is smooth
($C^\infty$), free from transition functions, and gauge equivariant. After
discussing some properties of this interpolation, we discuss the non-abelian
generalization of the method, arriving for SU(2), at a Cayley parametrization
of the links in terms of the Fourier modes of $A^c_\mu(x)$. We then discuss the
use of a maximum entropy type method to address gauge invariance in the
non-abelian case.


title: Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition

abstract:
  The QCD phase transition is studied on $16^3$ and $32^3 \times 4$ lattices
both with and without quark loops. We introduce a new zero-flavor or quenched
species of quark $\zeta$ and study the resulting chiral condensate, $\azbz$ as
a function of the $\zeta$ mass, $m_\zeta$. By examining $\azbz$ for $10^{-10}
\le m_\zeta \le 10$ we gain considerable information about the spectrum of
Dirac eigenvalues. A comparison of $ma=0.01$ and 0.025 shows little dependence
of the Dirac spectrum on such a light, dynamical quark mass, after an overall
shift in $\beta$ is removed. The presence of sufficient small eigenvalues to
support anomalous chiral symmetry breaking in the high temperature phase is
examined quantitatively. In an effort to enhance these small eigenvalues,
$\azbz$ is also examined in the pure gauge theory in the region of the
deconfinement transition with unexpected results. Above the critical
temperature, the three $Z_3$ phases show dramatically different chiral
behavior. Surprisingly, the real phase shows chiral symmetry, suggesting that a
system with one flavor of staggered fermion at $N_t=4$ will possess a chiral a
phase transition---behavior not expected in the continuum limit.


title: QCD with dynamical Wilson fermions - first results from SESAM

abstract:
  First results of a recently started simulation of full QCD with two flavours
of sea-quarks at a coupling of $\beta = 5.6$ on a $16^3 \times 32$ lattice are
presented. Emphasis is laid on the statistical significance that can be
achieved by an ``integrated luminosity'' of 140 TFlop$\times$hrs, for Hybrid
Monte Carlo simulations at four intermediate values of
$\frac{m_{\pi}}{m_{\rho}}$. The simulation takes place on the Quadrics QH2 at
DESY/Zeuthen and DFG/Bielefeld. The performance is optimized by means of
BiCGStab and the chronological inversion method of Brower et al. We discuss the
systematic errors arising from lack of the molecular dynamic's reversibility on
the 32-bit QH2. For plaquette and meson correlators we find integrated
autocorrelation times of $< 20$ units of molecular dynamics time and
exponential autocorrelation times of about $50$ units. Using these results we
perform preliminary measurements of the central potential and $\pi$ and $\rho$
correlators on independent configurations and obtain first estimates of the
lattice spacings at three values of the dynamical hopping parameter.


title: A Lattice Formulation of Chiral Gauge Theories

abstract:
  We present a method for formulating gauge theories of chiral fermions in
lattice field theory. The method makes use of a Wilson mass to remove doublers.
Gauge invariance is then restored by modifying the theory in two ways: the
magnitude of the fermion determinant is replaced with the square root of the
determinant for a fermion with vector-like couplings to the gauge field; a
double limit is taken, in which the lattice spacing associated with the fermion
field is sent to zero before the lattice spacing associated with the gauge
field. The method applies only to theories whose fermions are in an
anomaly-free representation of the gauge group. We also present a related
technique for computing matrix elements of operators involving fermion fields.
Although the analyses of these methods are couched in weak-coupling
perturbation theory, it is argued that the computational prescriptions are
gauge invariant in the presence of a nonperturbative gauge-field configuration.


title: A Real-Space Renormalization Group for Random Surfaces

abstract:
  We propose a new real-space renormalization group transformation for
dynamical triangulations. It is shown to preserve geometrical exponents such as
the string susceptibility and Hausdorff dimension. We furthermore show evidence
for a fixed point structure both in pure gravity and gravity coupled to a
critical Ising system. In the latter case we are able to extract estimates for
the gravitationally dressed exponents which agree to within 2-3% of the KPZ
formula.


title: Benchmark Test of CP-PACS for Lattice QCD

abstract:
  The CP-PACS is a massively parallel computer dedicated for calculations in
computational physics and will be in operation in the spring of 1996 at Center
for Computational Physics, University of Tsukuba. In this article, we describe
the architecture of the CP-PACS and report the results of the estimate of the
performance of the CP-PACS for typical lattice QCD calculations.


title:
Finite Temperature QCD with Wilson Quarks: A Study with a
  Renormalization Group Improved Gauge Action

abstract:
  Finite temperature transition in lattice QCD with degenerate Wilson quarks is
investigated on an $N_t=4$ lattice, using a renormalization group improved
gauge action. We find the following for the $N_F=2$ case:
  1) The transition is smooth for a wide range of the quark mass.
  2) The chiral transition is continuous.
  3) The chiral condensation well satisfies a scaling relation with the
critical exponents of the 3 dimensional $O(4)$ spin model. For $N_F=3$, we find
that the chiral transition is of first order.


title: Update on Quarkonium Spectroscopy and $\alpha_{strong}$ from NRQCD

abstract:
  NRQCD results for Upsilon and Charmonium using both dynamical and quenched
configurations are presented. We investigate dependence on the light dynamical
quark mass. Preliminary dynamical ($n_f = 2$) Charmonium data are combined with
quenched results to extract the strong coupling constant $\alpha_P^{(n_f)}$ for
the physical number of light dynamical quarks, $n_f = 3$. Good agreement is
found with calculations based on the Upsilon system. We show that a discrepancy
in $\alpha_P^{(n_f=0)}$, found between the Upsilon and Charmonium systems in
the quenched theory, disappears upon extrapolating to the physical number of
flavors. Results for the strong coupling constant $\alpha_{\overline{MS}}$ are
presented and sources of systematic error investigated.


title: Semileptonic Decays of D and B Mesons

abstract:
  We report results of our ongoing investigation concerning semileptonic decays
of heavy pseudoscalar mesons into pseudoscalar and vector mesons. Particular
attention is paid to uncertainties in the $q^2$ and the heavy quark mass
dependence of formfactors. Moreover we present a non-perturbative test to the
LMK current renormalization scheme for vector current transition matrix
elements and find remarkable agreement.


title: Lattice Quantum Gravity: Review and Recent Developments

abstract:
  We review the status of different approaches to lattice quantum gravity
indicating the successes and problems of each. Recent developments within the
dynamical triangulation formulation are then described. Plenary talk at LATTICE
95 July 11-15, Melbourne, Australia.


title: Effects of Improvement: $f_\pi$ and $m_q$

abstract:
  We present a study of the effects of improvement on light-quark physics using
the Fermilab formalism. The calculations were performed at three different
lattice spacings, with the SW action and traditional Wilson action (both
tadpole improved). We find that $O(a)$ effects for the decay constant $f_\pi$
and quark mass $m_q$ can be successfully removed using the tadpole-improved SW
action in the light-quark regime.


title: Renormalization of the Lattice Heavy Quark Classical Velocity

abstract:
  In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the
classical velocity is renormalized. The origin of this renormalization is the
reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The
renormalization is finite and depends on the form of the decretization of the
reduced heavy quark Dirac equation. For the Forward Time - Centered Space
discretization, the renormalization is computed both perturbatively, to one
loop, and non-perturbatively using an ensemble of lattices provided by the
Fermilab lattice collaboration. The estimates of the leading (linear) shift
agree, and indicate that for small classical velocities, the renormalized
velocity is reduced by about 25-30% relative to its bare (input) value.


title:
Chiral Symmetry Breaking in Strongly Coupled Quenched QED$_4$ Using the
  Dyson-Schwinger Equation Formalism

abstract:
  We study chiral symmetry breaking in quenched strong-coupling QED$_4$ in
arbitrary covariant gauge within the Dyson-Schwinger equation formalism. A
recently developed numerical renormalization program is fully implemented.
Results are compared for three different fermion-photon proper vertex {\it
Ans\"{a}tze\/}: bare $\gamma^\mu$, minimal Ball-Chiu, and Curtis-Pennington.
The procedure is straightforward to implement and numerically stable. We
discuss the chiral limit and observe that in this limit the renormalized axial
current is conserved. A detailed study of residual gauge dependence due to the
vertex choice is in progress. The relevance for lattice studies is discussed.


title:
Toward Precision Measurement of $B_K$ with Quenched Kogut-Susskind
  Quarks

abstract:
  We present a status report of our ongoing effort toward a precision
determination of the kaon $B$ parameter with the Kogut-Susskind quark action in
quenched QCD. Results for $B_K$ so far accumulated at $\beta =5.85$, 5.93, 6.0
and 6.2 corresponding to $a^{-1}=1.3-2.6$ GeV do not exhibit the theoretically
expected $O(a^2)$ behavior, but are apparently more consistent with an $O(a)$
behavior.


title:
Analysis of Hadron Propagators with One Thousand Configurations on a
  $24^3\times 64$ Lattice at $\beta=6.0$

abstract:
  Statistical properties of effective mass are analyzed. We show from a general
ground that effective mass as a function of time should not exhibit long
plateaux whatever high statistics simulations are made: the mass should
fluctuate beyond the one standard deviation of error bars after a few time
slices for large times where the ground state dominates. This explains the
difficulty of obtaining long plateaux experienced in previous simulations.
Implications of the observation for global $\chi^2$ fits are discussed, and
results for hadron masses are presented.


title:
Fate of the Critical Line and Chiral Transition in Finite-Temperature
  Lattice QCD with the Wilson Quark Action

abstract:
  Finite-temperature phase structure of lattice QCD with the Wilson quark
action is analyzed. We show that the critical line at finite temperatures,
defined to be the line of vanishing pion screening mass, turns back toward
strong coupling, forming a cusp on the $(\beta, K)$ plane, and that the line of
thermal transition runs past the tip of the cusp without touching the critical
line. Previous results are discussed in the light of our findings.


title: Four-Loop Perturbative Expansion for the Lattice $N$-Vector Model

abstract:
  We compute the four-loop contributions to the $\beta$-function and the
anomalous dimension of the field for the $O(N)$-invariant $N$-vector model.
These results are used to compute the second analytic corrections to the
correlation length and the general spin-$n$ susceptibility.


title: Decay rates of various bottomonium systems

abstract:
  Using the Bodwin--Braaten--Lepage factorization theorem in heavy quarkonium
decay and production processes, we calculated matrix elements associated with
S- and P-wave bottomonium decays via lattice QCD simulation methods. In this
work, we report preliminary results on the operator matching between the
lattice expression and the continuum expression at one loop level.
Phenomenological implications are discussed using these preliminary
\(\overline{MS}\) matrix elements.


title:
Non-Perturbative versus Perturbative Renormalization of Lattice
  Operators

abstract:
  Our objective is to compute the moments of the deep-inelastic structure
functions of the nucleon on the lattice. A major source of uncertainty is the
renormalization of the lattice operators that enter the calculation. In this
talk we compare the renormalization constants of the most relevant twist-two
bilinear quark operators which we have computed non-perturbatively and
perturbatively to one loop order. Furthermore, we discuss the use of tadpole
improved perturbation theory.


title:
The Phase Structure of the Schwinger Model on the Lattice with Wilson
  Fermions in the Hartree-Fock Approximation

abstract:
  The phase diagram of the Schwinger model on the lattice with one and two
degenerate flavours of Wilson fermions is investigated in the Hartree-Fock
approximation. In case of a single flavour (not directly amenable to numerical
simulation), the calculation indicates the existence of the parity violating
phase at both weak and intermediate-to-strong couplings. In the broken phase,
the Hartree-Fock vacuum sustains a nonzero electric field. With two flavours,
parity is not broken at weak coupling. However, both parity and flavour become
spontaneously broken at the Hartree-Fock level as the coupling becomes strong.


title: Width of Long Colour Flux Tubes in Lattice Gauge Systems

abstract:
  In the confining phase of any gauge system the mean squared width of the
colour flux tube joining a pair of quarks should grow logarithmically as a
function of their distance, according to the effective string description of
its infrared properties. New data on 3D Z_2 gauge theory, combined with high
precision data on the interface physics of the 3D Ising model fit nicely this
behaviour over a range of more than two orders of magnitude.


title: The Electroweak Phase Transition: A Non-Perturbative Analysis

abstract:
  We study on the lattice the 3d SU(2)+Higgs model, which is an effective
theory of a large class of 4d high temperature gauge theories. Using the exact
constant physics curve, continuum ($V\to\infty, a\to 0$) results for the
properties of the phase transition (critical temperature, latent heat,
interface tension) are given. The 3-loop correction to the effective potential
of the scalar field is determined. The masses of scalar and vector excitations
are determined and found to be larger in the symmetric than in the broken
phase. The vector mass is considerably larger than the scalar one, which
suggests a further simplification to a scalar effective theory at large Higgs
masses. The use of consistent 1-loop relations between 3d parameters and 4d
physics permits one to convert the 3d simulation results to quantitatively
accurate numbers for different physical theories, such as the Standard Model --
excluding possible nonperturbative effects of the U(1) subgroup -- for Higgs
masses up to about 70 GeV. The applications of our results to cosmology are
discussed.


title: The phase structure of pure Regge gravity

abstract:
  We examine the phase structure of pure Regge gravity in four dimensions and
compare our Monte Carlo results with $Z_2$-link Regge-theory as well as with
another formulation of lattice gravity derived from group theoretical
considerations. Within all three models we find an extension of the
well-defined phase to negative gravitational coupling and a new phase
transition. In contrast to the well-known transition at positive coupling there
is evidence for a continuous phase transition which might be essential for a
possible continuum limit.


title: Numerical Evidence for the Observation of a Scalar Glueball

abstract:
  We compute from lattice QCD in the valence (quenched) approximation the
partial decay widths of the lightest scalar glueball to pairs of pseudoscalar
quark-antiquark states. These predictions and values obtained earlier for the
scalar glueball's mass are in good agreement with the observed properties of
$f_J(1710)$ and inconsistent with all other observed meson resonances.


title: Improved lattice operators: the case of the topological charge density

abstract:
  We analyze the properties of a class of improved lattice topological charge
density operators, constructed by a smearing-like procedure. By optimizing the
choice of the parameters introduced in their definition, we find operators
having (i) a better statistical behavior as estimators of the topological
charge density on the lattice, i.e. less noisy; (ii) a multiplicative
renormalization much closer to one; (iii) a large suppression of the
perturbative tail (and other unphysical mixings) in the corresponding lattice
topological susceptibility.


title: Correlation functions between monopoles and instantons

abstract:
  We analyze the relation between instantons and abelian projected monopoles in
both phases of pure QCD by calculating local correlation functions between
topological charge densities and monopole densities. On an $8^{3} \times 4$
lattice, it turns out that topological quantities are correlated approximately
two lattice spacings. The monopole-instanton correlations are rather
insensitive under cooling of gauge fields.


title:
Lattice QCD Calculation of Flavor Singlet Matrix Elements and N-N
  Scattering Lengths

abstract:
  We report on our recent study of flavor singlet matrix elements calculated
with the wall source method without gauge fixing. Results are presented for the
mass difference between $\eta^{\prime}$ and pseudoscalar octet mesons, the
$\pi$-N $\sigma$ term and the proton axial vector matrix elements. An
exploratory calculation of the N-N scattering lengths is also discussed
including a phenomenological study with one-boson exchange potentials.


title: Perfect Lattice Actions for Quarks and Gluons

abstract:
  We use perturbation theory to construct perfect lattice actions for quarks
and gluons. The renormalized trajectory for free massive quarks is identified
by blocking directly from the continuum. We tune a parameter in the
renormalization group transformation such that for 1-d configurations the
perfect action reduces to the nearest neighbor Wilson fermion action. The fixed
point action for free gluons is also obtained by blocking from the continuum.
For 2-d configurations it reduces to the standard plaquette action. Classically
perfect quark and gluon fields, quark-gluon composite operators and vector and
axial vector currents are constructed as well. Also the quark-antiquark
potential is derived from the classically perfect Polyakov loop. The
quark-gluon and 3-gluon perfect vertex functions are determined to leading
order in the gauge coupling. We also construct a new block factor $n$
renormalization group transformation for QCD that allows to extend our results
beyond perturbation theory. For weak fields it leads to the same perfect action
as blocking from the continuum. For arbitrarily strong 2-d Abelian gauge fields
the Manton plaquette action is classically perfect for this transformation.


title:
Monopoles and Spatial String Tension in the High Temperature Phase of
  SU(2) QCD

abstract:
  We studied a behavior of monopole currents in the high temperature
(deconfinement) phase of abelian projected finite temperature SU(2) QCD in
maximally abelian gauge. Wrapped monopole currents closed by periodic boundary
play an important role for the spatial string tension which is a
non-perturbative quantity in the deconfinement phase. The wrapped monopole
current density seems to be non-vanishing in the continuum limit. These results
may be related to Polyakov's analysis of the confinement mechanism using
monopole gas in 3-dimensional SU(2) gauge theory with Higgs fields.


title: Casimir Scaling vs. Abelian Dominance in QCD String Formation

abstract:
  We show that the hypothesis of abelian dominance in maximal abelian gauge,
which is known to work for Wilson loops in the fundamental representation,
fails for Wilson loops in higher group representations. Monte Carlo simulations
are performed on lattice $SU(2)$ gauge theory, in $D=3$ dimensions, in the
maximal abelian gauge, in the confined phase. It is well-known that Creutz
ratios extracted from loops in various group representations are proportional
to the quadratic Casimir of each representation, in a distance interval from
the confinement scale to the point where color screening sets in. In contrast
we find numerically, in the same interval, that string tensions extracted from
loops built from abelian projected configurations are the same for the
fundamental and $j=3/2$ representations, and vanish for the adjoint
representation. In addition, we perform a lattice Monte Carlo simulation of the
Georgi-Glashow model in $D=3$ dimensions. We find that the
representation-dependence of string tensions is that of pure Yang-Mills in the
symmetric phase, but changes abruptly to equal tensions for the $j=1/2,~3/2$
representations, and zero tension for $j=1$, at the transition to the Higgs
phase. Our results indicate that an effective abelian theory at the confinement
scale, invoking {\it only} degrees of freedom (monopoles and photons)
associated with a particular Cartan subalgebra, is inadequate to describe the
actual interquark potential in an unbroken non-abelian gauge theory.


title: Absence of Physical Walls in Hot Gauge Theories

abstract:
  This paper shows that there are no {\em physical} walls in the deconfined,
high-temperature phase of $Z(2)$ lattice gauge theory. In a Hamiltonian
formulation, the interface in the Wilson lines is not physical. The line
interface and its energy are interpreted in terms of physical variables. They
are associated with a difference between two partition functions. One includes
only the configurations with even flux across the interface. The other is
restricted to odd flux. Also, with matter present, there is no physical
metastable state. However, the free energy is lowered by the matter. This
effect is described in terms of physical variables.