title: Thin Absolute Villains

abstract:
  We perform simulations of an absolute value version of the Villain model on
phi3 and phi4 Feynman diagrams, ``thin'' 3-regular and 4-regular random graphs.
The phi4 results are in excellent quantitative agreement with the exact
calculations by Dorey and Kurzepa for an annealed ensemble of thin graphs, in
spite of simulating only a single graph of each size. We also derive exact
results for an annealed ensemble of phi3 graphs and again find excellent
agreement with the numerical data for single phi3 graphs.
  The simulations confirm the picture of a mean field vortex transition which
is suggested by the analytical results. Further simulations on phi5 and phi6
graphs and of the standard XY model on phi3 graphs confirm the universality of
these results. The calculations of Dorey and Kurzepa were based on
reinterpreting the large orders behaviour of the anharmonic oscillator in a
statistical mechanical context so we also discuss briefly the interpretation of
singularities in the large orders behaviour in other models as phase
transitions.


title: Improved Actions for QCD Thermodynamics on the Lattice

abstract:
  Finite cut-off effects strongly influence the thermodynamics of lattice
regularized QCD at high temperature in the standard Wilson formulation. We
analyze the reduction of finite cut-off effects in formulations of the
thermodynamics of $SU(N)$ gauge theories with three different $O(a^2)$ and
$O(a^4)$ improved actions. We calculate the energy density and pressure on
finite lattices in leading order weak coupling perturbation theory
($T\rightarrow \infty$) and perform Monte Carlo simulations with improved
$SU(3)$ actions at non-zero $g^2$. Already on lattices with temporal extent
$N_\tau=4$ we find a strong reduction of finite cut-off effects in the high
temperature limit, which persists also down to temperatures a few times the
deconfinement transition temperature.


title: Meson-meson interactions -- from static to dynamic valence quarks

abstract:
  A method for the extraction of an effective meson-meson potential from Green
functions, which can be obtained from a lattice simulation, is presented.
Simulations are carried out for compact QED and QCD in four dimensions using
the quenched approximation and the hopping parameter expansion. In a further
study, a heavy-light meson is considered employing a conjugate gradient
algorithm for the light propagators. Due to the Pauli exclusion principle, the
results for QED indicate the existence of a hard core, but for QCD there is
strong attraction at small meson distances.


title: Heavy-Light Matrix Elements with the Wilson Quark Action

abstract:
  Status report is made of our quenched study of heavy-light matrix elements
employing the Wilson quark action for heavy quark. Results obtained up to now
with 200 configurations at $\beta=6.1$ on a $24^3\times64$ lattice and with 100
configurations at $\beta=6.3$ on a $32^3 \times80$ lattice suggest that the
pseudoscalar decay constant varies little over this range of $\beta$ in both
charm and bottom regions. Results for the $B$ parameter are also reported.


title: Non-perturbative Renormalization of Lattice Operators

abstract:
  We briefly review and compare three methods (one perturbative, one based on
Ward Identities and one non-perturbative) for the calculation of the
renormalization constants of lattice operators. The following results are
presented: (a) non perturbative renormalization of the operators with light
quarks; (b) the renormalization constants with a heavy (charm) quark mass and
its KLM improvement; (c) the non perturbative determination of the mixing of
the $\Delta S = 2$ operator.


title: Dual Abrikosov vortices in U(1) and SU(2) lattice gauge theories

abstract:
  The spatial distribution of fields and currents in confining theories can
give direct evidence of dual superconductivity. We review the behavior of
vortices in the lattice Higgs effective theory. We discuss the techniques for
finding these properties and calculating the superconductivity parameters in
lattice simulations. We have seen dual Abrikosov vortices directly in pure U(1)
and SU(2) and others have also seen them in SU(3). We review the duality
transformation for U(1) in order to connect the U(1) results to a dual Higgs
theory.
  In the non-Abelian cases the system appears to be near the borderline between
type I and II. We also discuss the response of the persistent currents to
external fields.


title: Weak Matrix Elements on the Lattice --- Circa 1995

abstract:
  Status of weak matrix elements is reviewed. In particular, $\epspeps$,
$\bkastg$, $B_K$, $B_B$ and $B_{B_s}$ are discussed and the overall situation
with respect to the lattice effort and some of its phenomenological
implications are summarized. For $\epspeps$ the need for the relevant matrix
elements is stressed in view of the forthcoming improved experiments. For some
of the operators, (e.g.\ $O_6$), even bounds on their matrix elements would be
very helpful. On $\bkastg$, a constant behavior of $T_2$ appears disfavored
although dependence of $T_2$ could, of course, be milder than a simple pole.
Improved data is badly needed to settle this important issue firmly, especially
in view of its ramification for extractions of $V_{td}$ from $B\to\rho\gamma$.
On $B_K$, the preliminary result from JLQCD appears to contradict Sharpe \etal\
JLQCD data seems to fit very well to linear $a$ dependence and leads to an
appreciably lower value of $B_K$. Four studies of $B_K$ in the ``full''
($n_f=2$) theory indicate very little quenching effects on $B_K$; the full
theory value seems to be just a little less than the quenched result. Based on
expectations from HQET, analysis of the $B$-parameter ($B_{h\ell}$) for the
heavy-light mesons via
$B_{h\ell}={}$constant${}+{}$constants$^\prime/m_{h\ell}$ is suggested. A
summary of an illustrative sample of hadron matrix elements is given and
constraints on CKM parameters (e.g.\ $V_{td}/V_{ts}$), on the unitarity
triangle and on $x_s/x_d$, emerging from the lattice calculations along with
experimental results are briefly discussed. In quite a few cases, for the first
time, some indication of quenching errors on weak matrix elements are now
becoming available.


title: Quenched Chiral Perturbation Theory for Heavy-light Mesons

abstract:
  We formulate quenched chiral perturbation theory for heavy-light mesons
coupled to pions, and calculate the one-loop chiral logarithmic corrections to
$f_B$, $f_{B_{s}}$, $B_B$ and $B_{B_{s}}$. We also calculate these corrections
for ``partially quenched'' theories. In both theories, the chiral logarithms
diverge in the chiral limit, indicating that (partially) quenched theories
should not be used to study this limit. Comparing the chiral logarithms to
those in QCD, we estimate the errors caused by (partial) quenching. By forming
suitable ratios, we can reduce the uncertainties in our estimates.


title: The Eta-prime and Cooling with Staggered Fermions

abstract:
  We present a calculation of the mass of the eta-prime meson using quenched
and dynamical staggered fermions. We also discuss the effects of "cooling" and
suggest its use as a quantitative tool.


title:
QCD phase transition with two flavors of Wilson quarks using a RG
  improved action

abstract:
  The finite temperature QCD phase transition is studied on the lattice with
degenerate two flavors of Wilson quarks. Motivated by reported strange
behaviors with the standard action on lattices with the temporal extention
$N_t=4$ and 6, a renormalization group improved gauge action is applied. On an
$N_t=4$ lattice, the strange behaviors observed with the standard action are
removed with our improved action. The finite temperature transition is
continuous in the chiral limit and it becomes quite smooth in all observables
we studied when we increase the quark mass by increasing $\beta$ along the
crossover line.


title: Finite Temperature QCD on the Lattice

abstract: Recent progress in lattice QCD at finite temperature is reviewed.


title: Correlations and Binding in 4D Dynamical Triangulation

abstract:
  We study correlations on the euclidean spacetimes generated in Monte Carlo
simulations of the model. In the elongated phase, curvature correlations appear
to fall off like a fractional power. Near the transition to the crumpled phase
this power is consistent with 4. We also present improved data of our
computations of the binding energy of test particles.


title: An Algorithm for Gluinos on the Lattice

abstract:
  L\"uscher's local bosonic algorithm for Monte Carlo simulations of quantum
field theories with fermions is applied to the simulation of a possibly
supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint
representation. Combined with a correction step in a two-step polynomial
approximation scheme, the obtained algorithm seems to be promising and could be
competitive with more conventional algorithms based on discretized classical
(``molecular dynamics'') equations of motion. The application of the considered
polynomial approximation scheme to optimized hopping parameter expansions is
also discussed.


title: A Lattice Chiral Gauge Theory with Multifermion Couplings

abstract:
  Analyzing an $SU_L(2)$-chiral gauge theory with external multifermion
couplings, we find a possible scaling region where doublers decouple by
acquiring chiral-invariant masses and $\psi_R$ is free mode owing to the
$\psi_R$-shift-symmetry, the chiral continuum theory of $\psi^i_L$ can be
defined. This is not in agreement with the general belief of the failure of
theories so constructed .


title: Decay constants with Wilson fermions at $\beta=6.0$

abstract:
  We present results of a high statistics study of $f_\pi$, $f_K$, $f_D$,
$f_{D_s}$, and $f_V^{-1}$ in the quenched approximation using Wilson fermions
at $\beta=6.0$ on $32^3 \times 64$ lattices. We find that the various sources
of systematic errors (due to setting the quark masses, renormalization
constant, and lattice scale) are now larger than the statistical errors. Our
best estimates, without extrapolation to the continuum limit, are $f_\pi=134(4)
\MeV$, $f_K =159(3) \MeV$, $f_D = 229(7) \MeV$, $f_{D_s} = 260(4) \MeV$, and
$f_V^{-1}(m_\rho) = 0.33(1)$, where only statistical errors have been shown. We
discuss the extrapolation to the continuum limit by combining our data with
those from other collaborations.


title: The Strong Coupling Constant from the Lattice 3-Gluon Vertex

abstract:
  We compute the QCD running coupling on the lattice as defined from the
3-gluon vertex. We present the results of an exploratory study at $\beta=6.0$
on a $16^4$ lattice, which show that for momenta larger than 2 \Gev, the
coupling runs according to the 2-loop asymptotic formula, allowing a precise
determination of the $\Lambda$ parameter. Our renormalization procedure
corresponds to a momentum subtraction scheme in the continuum and, most
remarkably, one does not need lattice perturbation theory to match the results
to MSbar scheme. We obtain $\alpha^{\MSB}(M_Z) = 0.115 \pm 0.003 \pm 0.008$.


title: Comments on Lattice Calculations of Proton Spin Components

abstract:
  Comments on the recent lattice QCD calculations of the flavor-singlet axial
coupling constant $g_A^0$ and individual quark and gluon spin contributions to
the proton spin is given. I point out the physics learned from these
calculations as well as some of the lessons and pitfalls.


title:
New Developments in Lattice QCD: Calculation of Flavor Singlet Nucleon
  Matrix Elements and Hadron Scattering Lengths

abstract:
  Recent developments in lattice QCD calculation of flavor singlet nucleon
matrix elements are reviewed. Substantial sea quark contributions are found in
the $\pi$-$N\ \sigma$ term and the quark spin content of the nucleon such that
the total magnitude including valence contributions is in reasonable agreement
with experiments. Some problems with flavor non-singlet nucleon matrix elements
are pointed out. Recent work on lattice QCD calculation of hadron scattering
length is also discussed.


title: Light meson decay constants beyond the quenched approximation

abstract:
  We calculate the effects of including dynamical fermion loops in the lattice
QCD estimates of meson decay constants, by extrapolating the results from
negative flavour numbers after a suitable matching of the pion and rho mass.
For moderately light quarks, the values of the decay constants not corrected
for the renormalization constants increase with respect to their quenched
values.


title: QCD for Coarse Lattices

abstract:
  This is the Lattice '95 review of recent progress towards accurate QCD
simulations using very coarse lattices. This development could have
revolutionary implications for low energy (nonperturbative) QCD.


title:
Monte Carlo Simulations of Conformal Theory Predictions for the 3-state
  Potts and Ising Models

abstract:
  The critical properties of the 2D Ising and 3-state Potts models are
investigated using Monte Carlo simulations. Special interest is given to
measurement of 3-point correlation functions and associated universal objects,
i.e. structure constants. The results agree well with predictions coming from
conformal field theory confirming, for these examples, the correctness of the
Coulomb gas formalism and the bootstrap method.


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

abstract:
  The renormalized trajectory in the multi-dimensional coupling parameter space
of the two-dimensional O(3) non-linear sigma model is determined numerically
under \linebreak $\delta$-function block spin transformations using two
different Monte Carlo renormalization group techniques. The renormalized
trajectory is compared with the straight line of the fixed point trajectory
(fixed point action) which leaves the asymptotically free ultraviolet fixed
point of the critical surface in the orthogonal direction. Our results show
that the renormalized trajectory breaks away from the fixed point trajectory in
a range of the correlation length around $\xi \approx 3$-$7$, flowing into the
high temperature fixed point at $\xi=0$. The analytic large $N$ calculation of
the renormalized trajectory is also presented in the coupling parameter space
of the most general bilinear Hamiltonians. The renormalized trajectory in the
large $N$ approximation exhibits a similar shape as in the $N=3$ case, with the
sharp break occurring at a smaller correlation length of $\xi \approx 2$-$3$.


title:
$B_c$ and $\Upsilon$ Spectra from Lattice NRQCD - Results at $\beta$ =
  5.7

abstract:
  We update our results for the heavy-heavy spectrum at $\beta$ = 5.7, using
NRQCD. This includes a scaling comparison with the $\Upsilon$ spectrum at
$\beta$ = 6.0 and first lattice predictions for the $B_c$ spectrum.


title:
Excited states in the full QCD hadron spectrum on a $16^3 \times 40$
  lattice

abstract:
  We report the hadron mass spectrum obtained on a $16^3 \times 40$ lattice at
$\beta = 5.7$ using two flavors of staggered fermions with $m a = 0.01$. We
calculate the masses of excited states that have the same quantum numbers as
the $\pi$, $\rho$ and $N$. They are obtained by a combined analysis of the
hadron correlators from sources of size $16^3$ and $8^3$. We also report on the
hadron spectrum for a wide range of valence quark masses.


title:
Analysis of saddle-point configurations in 3-dimensional SU(2) gauge
  theory

abstract:
  We discuss the properties of a class of saddle point solutions in SU(2) in
three dimensions (SU$(2)_3$), exhibiting localized peaks in the action. These
configurations are generated by deterministic cooling and extremizing
algorithms from analytic configurations. They share some characteristics with
cooled and extremized Monte Carlo generated lattices. We have investigated
physical behavior such as the string tension by averaging over this class of
saddle point configurations. We have also measured the eigenvalues for harmonic
fluctuations around these configurations.


title: A Lecture on Chiral Fermions

abstract:
  This is an informal and approximate transcription of a talk presented at the
DESY workshop, September 27--29, 1995. The basic message is that real and long
overdue progress is taking place on the problem of regulating
non--perturbatively chiral gauge theories. Several approaches are reviewed with
emphasis on the overlap and some of the questions raised about it. No claim for
completeness or objectivity is made.


title: Results from Lattice QCD for baryons containing a heavy quark

abstract:
  We present the calculation of the spectrum of baryons containing one heavy
quark. Heavy baryon and meson mass splittings are computed and compared with
experiment. We give preliminary results for the form factor $G_1$ for the
semileptonic decay $ \Lambda_b \rightarrow \Lambda_c l \bar{\nu} $ and
investigate its flavour symmetry.


title:
New Universality Class in three dimensions: the Antiferromagnetic $RP^2$
  model

abstract:
  We present the results of a Monte Carlo simulation of the $RP^2$ model in
three dimensions with negative coupling. We observe a second order phase
transition between the disordered phase and an antiferromagnetic, unfrustrated,
ordered one. We measure, with a Finite Size Scaling analysis, the thermal
exponent, obtaining $\nu=0.784(8)$. We have found two magnetic-type relevant
operators whose related $\eta$ exponents are $0.038(2)$ and $1.338(8)$
respectively.


title:
Tests of the continuum limit for the $SO(4)$ Principal Chiral Model and
  the prediction for $\L_\MS$

abstract:
  We investigate the continuum limit in $SO(N)$ Principal Chiral Models
concentrating in detail on the $SO(4)$ model and its covering group
SU(2)xSU(2). We compute the mass gap in terms of Lambda_MS and compare with the
prediction of Hollowood of $m/\L_\MS = 3.8716$. We use the finite-size scaling
method of L\"uscher et al. to deduce $m/\L_\MS$ and find that for the $SO(4)$
model the computed result of $m/\L_\MS \sim 14$ is in strong disagreement with
theory but that a similar analysis of the SU(2)xSU(2) yields excellent
agreement with theory. We conjecture that for $SO(4)$ violations of the
finite-size scaling assumption are severe forthe values of the correlation
length, $\xi$, investigated and that our attempts to extrapolate the results to
zero lattice spacing, although plausible, are erroneous. Conversely, the
finite-size scaling violations in the SU(2)xSU(2) simulation are consistent
with perturbation theory and the computed $beta-$function agrees well with the
3-loop approximation for couplings evaluated at scales $L/a \le \xi$, where
$\xi$ is measured in units of the lattice spacing, $a$. We conjecture that
lattice vortex artifacts in the $SO(4)$ model are responsible for delaying the
onset of the continuum limit until much larger correlation lengths are achieved
notwithstanding the apparent onset of scaling. Results for the mass spectrum
for SO(N) m, N=8,10 are given whose comparison with theory gives plausible
support to our ideas.


title: Interplay of universality classes in a three-dimensional Yukawa model

abstract:
  We investigate numerically on the lattice the interplay of universality
classes of the three-dimensional Yukawa model with U(1) chiral symmetry, using
the Binder method of finite size scaling. At zero Yukawa coupling the scaling
related to the magnetic Wilson--Fisher fixed point is confirmed. At
sufficiently strong Yukawa coupling the dominance of the chiral fixed point
associated with the 3D Gross--Neveu model is observed for various values of the
coupling parameters, including infinite scalar selfcoupling. In both cases the
Binder method works consistently in a broad range of lattice sizes. However,
when the Yukawa coupling is decreased the finite size behavior gets complicated
and the Binder method gives inconsistent results for different lattice sizes.
This signals a cross-over between the universality classes of the two fixed
points.


title: Adjoint ``Quarks'' and the Physics of Confinement

abstract:
  The quark-antiquark potential and the chromoelectric fields generated by
``quarks'' in the adjoint representation of SU(2) color are analyzed in the
scaling region of the theory. New results with interesting implications for our
understanding of the confinement mechanism are presented. In particular, the
formation of color-electric flux-tubes between adjoint quarks is demonstrated
in four-dimensional SU(2) color. The flux-tubes for fundamental and adjoint
representation quarks are shown to have very similar cross-sections. This
result could imply that the QCD vacuum is dual to a type I superconductor.


title: Deconfinement, Screening and Abelian Projection at Finite Temperature

abstract:
  The behavior of static sources transforming according to different
irreducible representations of the gauge group is studied in the context of
finite temperature lattice gauge theory. We combine analytical and numerical
approaches to extract information about confinement and screening both at low
temperatures, and around the deconfinement phase transition. The idea that
abelian projection in the Maximally Abelian Gauge reproduces the most important
features of confinement and screening is tested at a quantitative level in
these finite-T theories. Our results show that while this abelian projection
provides correct qualitative features, it fails at a detailed quantitative
level.


title: Chiral Symmetry Breaking and Cooling in Lattice QCD

abstract:
  Chiral symmetry breaking is calculated as a function of cooling in quenched
lattice QCD. A non-zero signal is found for the chiral condensate beyond one
hundred cooling steps, suggesting that there is chiral symmetry breaking
associated with instantons. Quantitatively, the chiral condensate in cooled
gauge field configurations is small compared to the value without cooling.


title:
Numerical analysis of the spectrum of the Dirac operator in
  four-dimensional SU(2) gauge fields

abstract:
  Two numerical algorithms for the computation of eigenvalues of Dirac
operators in lattice gauge theories are described: one is an accelerated
conjugate gradient method, the other one a standard Lanczos method. Results
obtained by Cullum's and Willoughby's variant of the Lanczos method (whose
convergence behaviour is closely linked with the local spectral density) are
presented for euclidean Wilson fermions in quenched and unquenched SU(2) gauge
fields. Complete spectra are determined on lattices up to $8^3 \cdot 12$, and
we derive numerical values for fermionic determinants and results for spectral
densities.


title: Some properties of B_c from Lattice QCD

abstract:
  We discuss \(B_c\) mass (1S state) and decay constant \(f_{B_c}\) calculated
by lattice non-relativistic quantum chromodynamcs(NRQCD) method. In leading
order of \(v^2\), we found that \(M_{B_c} = 6.33(2)\) GeV and \(f_{B_c} =
395(2)\) MeV where the error bar is the statistical error only. Using these
values, we estimate QCD effects to leptonic decay width of \(B_c\). The decay
width is given by \(\Gamma(B_c \rightarrow l^+\nu_l) = 0.86(15)m^2_l (1 -
0.0250(2)m^2_l)^2\times 10^{-14} ({\rm GeV})\), where \(m_l\) is in GeV.
Relativistic correction and \(\alpha_s\) correction to \(f_{B_c}\) have also
been considered.


title: Spectral Density on the Lattice

abstract:
  Spectral density in the pseudoscalar and vector channels is extracted from
the SU(2) lattice quenched data. It is shown to consist of three sharp poles
within the energy range accessible on the lattice.


title: Glue Ball Masses and the Chameleon Gauge

abstract:
  We introduce a new numerical technique to compute mass spectra, based on
difference method and on a new gauge fixing procedure. We show that the method
is very effective by test runs on a $SU(2)$ lattice gauge theory.


title: Recent Results on the Nucleon Structure Functions from Lattice QCD

abstract:
  We report on recent results of a high statistics lattice calculation of the
unpolarized and polarized structure functions of the nucleon.


title:
Non-compact Lattice QED with Two Charges: Phase Diagram and
  Renormalization Group Flow

abstract:
  The phase diagram of non-compact lattice QED in four dimensions with
staggered fermions of charges 1 and $-1/2$ is investigated. The renormalized
charges are determined and found to be in agreement with perturbation theory.
This is an indication that there is no continuum limit with non-vanishing
renormalized gauge coupling, and that the theory has a validity bound for every
finite value of the renormalized coupling. The renormalization group flow of
the charges is investigated and an estimate for the validity bound as a
function of the cut-off is obtained. Generalizing this estimate to all fermions
in the Standard Model,it is found that a cut-off at the Planck scale implies
that $\alpha_R$ has to be less than $1/80$. Due to spontaneous chiral symmetry
breaking, strongly bound fermion-antifermion composite states are generated.
Their spectrum is discussed.


title:
Deconfinement transition and dimensional cross-over in the 3D gauge
  Ising model

abstract:
  We present a high precision Monte Carlo study of the finite temperature $Z_2$
gauge theory in 2+1 dimensions. The duality with the 3D Ising spin model allows
us to use powerful cluster algorithms for the simulations. For temporal
extensions up to $N_t=16$ we obtain the inverse critical temperature with a
statistical accuracy comparable with the most accurate results for the bulk
phase transition of the 3D Ising model. We discuss the predictions of T. W.
Capehart and M.E. Fisher for the dimensional crossover from 2 to 3 dimensions.
Our precise data for the critical exponents and critical amplitudes confirm the
Svetitsky-Yaffe conjecture. We find deviations from Olesen's prediction for the
critical temperature of about 20%.


title: Instantons and Monopoles in the Maximally Abelian Gauge

abstract:
  We study the Abelian projection of SU(2) instantons in the Maximally Abelian
gauge. We find that in this gauge an isolated instanton produces a closed
monopole loop within its core and the size of this loop increases with the core
size. We show that this result is robust against the introduction of small
quantum fluctuations. We investigate the effects of neighbouring
(anti)instantons upon each other and show how overlapping (anti)instantons can
generate larger monopole loops. We find, however, that in fields that are
typical of the fully quantised vacuum only some of the large monopole loops
that are important for confinement have a topological origin. We comment on
what this may imply for the role of instantons in confinement and chiral
symmetry breaking.


title: Lattice Investigations of the Running Coupling

abstract:
  A review of investigations of running couplings using lattice techniques is
given. This includes i) studies of the running of particular non-perturbatively
defined renormalized couplings in pure gauge theories over a range of energies,
and ii) how estimates of $\alpha_{\overline{MS}}(m_Z)$ in lattice QCD are
presently obtained.


title: Testing the Quasi-temporal Gauge on the Lattice

abstract:
  We investigate the viability of the quasi-temporal gauge on the lattice. This
is a complete gauge fixing condition that can be implemented on the lattice at
a very low computational cost. As a test case, using the Clover action, we have
evaluated the (gauge invariant) renormalisation constant of the non-singlet
axial current, using Ward identities extracted from quark states. Our result is
in reasonable but not complete agreement with previous values obtained from
Ward identities both on hadronic states and on quark states in the Landau
gauge. We observe large fluctuations due to lattice Gribov copies. The
influence of finite volume effects is expected to be non-negligible in the case
we are considering.


title: Lattice Schwinger Model with interpolated Gauge Fields

abstract:
  We analyze the Schwinger model on an infinite lattice using the continuum
definition of the fermion determinant and a linear interpolation of the lattice
gauge fields. The possible class of interpolations for the gauge fields,
compatible with gauge invariance is discussed. The effective action for the
lattice gauge field is computed for the Wilson formulation as well as for
non-compact lattice gauge fields. For the non-compact formulation we prove that
the model has a critical point with diverging correlation length at zero gauge
coupling e. We compute the chiral condensate for e > 0 and compare the result
to the N-flavor continuum Schwinger model. This indicates that there is only
one flavor of fermions with the same chiral properties as in the continuum
model, already before the continuum limit is performed. We discuss how
operators have to be renormalized in the continuum limit to obtain the
continuum Schwinger model.


title: Critical Slowing-Down in $SU(2)$ Landau Gauge-Fixing Algorithms

abstract:
  We study the problem of critical slowing-down for gauge-fixing algorithms
(Landau gauge) in $SU(2)$ lattice gauge theory on a $2$-dimensional lattice. We
consider five such algorithms, and lattice sizes ranging from $8^{2}$ to
$36^{2}$ (up to $64^2$ in the case of Fourier acceleration). We measure four
different observables and we find that for each given algorithm they all have
the same relaxation time within error bars. We obtain that: the so-called {\em
Los Alamos} method has dynamic critical exponent $z \approx 2$, the {\em
overrelaxation} method and the {\em stochastic overrelaxation} method have $z
\approx 1$, the so-called {\em Cornell} method has $z$ slightly smaller than
$1$ and the {\em Fourier acceleration} method completely eliminates critical
slowing-down. A detailed discussion and analysis of the tuning of these
algorithms is also presented.


title:
Renormalization group flow and fixed point of the lattice topological
  charge in the 2-d O(3) sigma-model

abstract:
  We study the renormalization group evolution up to the fixed point of the
lattice topological susceptibility in the 2-d O(3) non-linear sigma-model. We
start with a discretization of the continuum topological charge by a local
charge density, polynomial in the lattice fields. Among the different choices
we propose also a Symanzik--improved lattice topological charge. We check step
by step in the renormalization group iteration the progressive dumping of
quantum fluctuations, which are responsible for the additive and multiplicative
renormalizations of the lattice topological susceptibility with respect to the
continuum definition. We find that already after three iterations these
renormalizations are negligible and an excellent approximation of the fixed
point is achieved. We also check by an explicit calculation that the assumption
of slowly varying fields in iterating the renormalization group does not lead
to a good approximation of the fixed point charge operator.


title:
Dynamic Critical Behavior of a Swendsen-Wang-Type 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, and is
almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears
to tend to infinity either as a logarithm or as a small power ($0.05 \leq p
\leq 0.12$). In an appendix we discuss the problem of extracting estimates of
the exponential autocorrelation time.


title:
Singular Vertices in the Strong Coupling Phase of Four--Dimensional
  Simplicial Gravity

abstract:
  We study four--dimensional simplicial gravity through numerical simulation
with special attention to the existence of singular vertices, in the strong
coupling phase, that are shared by abnormally large numbers of four--simplices.
The second order phase transition from the strong coupling phase into the weak
coupling phase could be understood as the disappearance of the singular
vertices. We also change the topology of the universe from the sphere to the
torus.


title: Long range correlations in branched polymers

abstract:
  We study the correlation functions in the branched polymer model. Although
there are no correlations in the grand canonical ensemble, when looking at the
canonical ensemble we find negative long range power like correlations. We
propose that a similar mechanism explains the shape of recently measured
correlation functions in the elongated phase of 4d simplicial gravity.


title: Polarized Nucleon Structure Functions from Lattice QCD

abstract:
  We describe a high statistics quenched QCD calculation of the moments of the
polarized deep-inelastic structure functions g_1 and g_2 of the proton and
neutron.


title:
Pathologies of Quenched Lattice QCD at non--zero Density and its
  Effective Potential

abstract:
  We simulate lattice QCD at non--zero baryon density and zero temperature in
the quenched approximation, both in the scaling region and in the infinite
coupling limit. We investigate the nature of the forbidden region -- the range
of chemical potential where the simulations grow prohibitively expensive, and
the results, when available, are puzzling if not unphysical. At weak coupling
we have explored the sensitivity of these pathologies to the lattice size, and
found that using a large lattice ($64 \times 16^3$) does not remove them. The
effective potential sheds considerable light on the problems in the
simulations, and gives a clear interpretation of the forbidden region. The
strong coupling simulations were particularly illuminating on this point.


title: Lattice Heavy Quark Effective Theory and the Isgur-Wise function

abstract:
  We compute the Isgur-Wise function using heavy quark effective theory
formulated on the lattice. The non-relativistic kinetic energy term of the
heavy quark is included to the action as well as terms remaining in the
infinite quark mass limit. The classical velocity of the heavy quark is
renormalized on the lattice and we determine the renormalized velocity
non-perturbatively using the energy-momentum dispersion relation. The slope
parameter of the Isgur-Wise function at zero recoil is obtained at $\beta=6.0$
on a $24^3\times 48$ lattice for three values of $m_{Q}$.


title: The Chiral Dirac Determinant According to the Overlap Formalism

abstract:
  The chiral Dirac determinant is calculated using the overlap formalism of
Narayanan and Neuberger. We compare the real and imaginary parts of the
determinant with the continuum result for perturbative gauge field backgrounds
and show that they are identical. Thus we find that the overlap formalism
passes a crucial test.


title:
Measuring the string susceptibility in 2D simplicial quantum gravity
  using the Regge approach

abstract:
  We use Monte Carlo simulations to study pure 2D Euclidean quantum gravity
with $R^2$-interaction on spherical topologies, employing Regge's formulation.
We attempt to measure the string susceptibility exponent $\gamma_{\rm str}$ by
using a finite-size scaling Ansatz in the expectation value of $R^2$, as has
been done in a previous study by Bock and Vink ( hep-lat/9406018 ). By
considerably extending the range and statistics of their study we find that
this Ansatz is plagued by large systematic errors. The $R^2$ specific string
susceptibility exponent $\GS'$ is found to agree with theoretical predictions,
but its determination also is subject to large systematic errors and the
presence of finite-size scaling corrections. To circumvent this obstacle we
suggest a new scaling Ansatz which in principle should be able to predict both,
$\GS$ and $\GS'$. First results indicate that this requires large system sizes
to reduce the uncertainties in the finite-size scaling Ans\"atze. Nevertheless,
our investigation shows that within the achievable accuracy the numerical
estimates are still compatible with analytic predictions, contrary to the
recent claim by Bock and Vink.


title: Observing instantons directly on the lattice without cooling

abstract:
  Based on the study of the simple Abelian Higgs model in $1+1$ dimensions we
will present a new method to identify and localize extended instantons. The
idea is to measure the topological charge on regions somewhat larger than the
extended instantons so as to average out the ultraviolet fluctuations but
without losing the detailed topological information when going to the full
space. The instanton size and probability density can be directly extracted
from this analysis. Local dislocations, which can be avoided for fine enough
lattices, can be reinterpreted as modified boundary conditions producing
sectors with net topological charge.


title: The Landshoff-Nachtmann Pomeron on the Lattice

abstract:
  We investigate the Landshoff-Nachtmann two-gluon-exchange model of the
Pomeron using gluon propagators computed in the Landau gauge within quenched
lattice QCD calculations. We first determine an effective gluon-quark coupling
by constraining the Pomeron-quark coupling to its phenomenological value
$\beta_0 = 2\, \gev^{-1}$. We then provide predictions for a variety of
diffractive processes. As the propagators have been evaluated entirely from QCD
first principles (although in the quenched approximation), our results provide
a consistency check of the Landshoff-Nachtmann model. We address the issue of
the possible gauge-dependence of our results, which will be the object of a
future study.


title: Improvements of L\"uscher's local bosonic fermion algorithm

abstract:
  We discuss the application of hybrid over-relaxation, even-odd
preconditioning and a modified local updating procedure to the local bosonic
fermion algorithm. Studies on autocorrelation times and the tuning of the
parameters of the algorithm are done on various lattice sizes simulating
SU(2)-LGT with 2 flavours of Wilson quarks. A substantial decrease of the
computational cost could be achieved.


title: Ising Spins on a Gravitating Sphere

abstract:
  We investigated numerically an Ising model coupled to two-dimensional
Euclidean gravity with spherical topology, using Regge calculus with the $dl/l$
path-integral measure to discretize the gravitational interaction. Previous
studies of this system with toroidal topology have shown that the critical
behavior of the Ising model remains in the flat-space Onsager universality
class, contrary to the predictions of conformal field theory and matrix models.
Implementing the spherical topology as triangulated surfaces of
three-dimensional cubes, we find again strong evidence that the critical
exponents of the Ising transition are consistent with the Onsager values, and
that KPZ exponents are definitely excluded.


title:
First Lattice Study of Ghost Propagators in SU(2) and SU(3) Gauge
  Theories

abstract:
  We present a numerical study of the ghost propagators in Landau gauge for
SU(2) and SU(3) gauge theories at $\beta$=2.7 and $\beta$=6.0, respectively.
Analyzing different lattice sizes up to $32^4$, we find small finite size
effects. Down to the smallest available momenta, we observe no evidence for
dipole behaviour of the ghost propagators.


title: The electroweak sphaleron on the lattice

abstract:
  We study the properties of the electroweak sphaleron on a finite lattice. The
cooling algorithm for saddle points is used to obtain the static classical
solutions of the SU(2)-Higgs field theory. Results are presented for
$M_H=\infty, M_W, 0.75M_W$. After performing finite size scaling we find good
agreement with the results obtained from variational approaches. Of relevance
for numerical determinations of the transition rate is that the lattice
artefacts are surprisingly small for $M_W\approx M_H$.


title: Testing the chiral behavior of the hadron spectrum

abstract:
  We analyze the chiral behavior of the hadron spectrum obtained with quenched
Wilson fermions on 170 $32^3 \times 64$ lattices at $\beta = 6.0$. We calculate
masses of hadrons composed of both degenerate and non-degenerate quarks. We
reduce the statistical errors in mass splittings by directly fitting to the
ratio of correlation functions. We find significant deviations from a linear
dependence on the quark mass, deviations that are consistent with the higher
order terms predicted by quenched chiral perturbation theory. Including these
corrections yields splittings in the baryon octet that agree with those
observed experimentally. Smaller higher order terms are also present in
$m_\rho$ and $m_N$. By contrast, the decuplet baryons are well described by a
linear mass term. We find the decuplet splittings to be 30% smaller than
experiment. We extrapolate our data to $a \to 0$ by combining with the GF11
results, and the best fit suggests that the quenched approximation is only good
to $10-15%$.


title: Status Report on Weak Matrix Element Calculations

abstract:
  This talk presents results of weak matrix elements calculated from
simulations done on 170 $32^3 \times 64$ lattices at $\beta = 6.0$ using
quenched Wilson fermions. We discuss the extraction of pseudoscalar decay
constants $f_\pi$, $f_K$, $f_D$, and $f_{D_s}$, the form-factors for the rare
decay $B \to K^* \gamma$, and the matrix elements of the 4-fermion operators
relevant to $B_K$, $B_7$, $B_8$. We present an analysis of the various sources
of systematic errors, and show that these are now much larger than the
statistical errors for each of these observables. Our main results are
$f_D=186(29) \MeV$, $f_{D_s}=224(16) MeV$, $T_1=T_2=0.24(1)$, $B_K(NDR,
2\GeV)=0.67(9)$, and $B_8(NDR, 2\GeV)=0.81(1)$.


title: Lattice analysis of semi-leptonic form factors

abstract:
  We present preliminary results from simulations done on 170 $32^3 \times 64$
lattices at $\beta = 6.0$ using quenched Wilson fermions. This talk focuses on
the $Q^2$ behavior of the form-factors, extrapolation in quark masses,
dependence on renormalization scheme, and comparison with heavy-quark effective
theory (HQET). Even though we cannot estimate errors due to quenching and
discretization, our results are consistent with experimental results for $D$
decays. We present results for the Isgur-Wise function and estimate $\xi'(w=1)
= 0.97(6)$.


title:
Confinement Mechanism in Various Abelian Projections of Lattice
  Gluodynamics

abstract:
  We show that the monopole confinement mechanism in lattice gluodynamics may
be a particular feature of the maximal abelian projection. We give an explicit
example of the $SU(2) \rightarrow U(1)$ projection (the minimal abelian
projection), in which the confinement is due to topological objects other than
monopoles. We also discuss the string representation of the abelian projected
$SU(2)$ gluodynamics.


title: Non-perturbative renormalization of lattice QCD at all scales

abstract:
  A general strategy to solve the non-perturbative renormalization problem in
lattice QCD, using finite-size techniques and numerical simulations, is
described. As an illustration we discuss the computation of the axial current
normalization constant, the running coupling at zero quark masses and the scale
evolution of the renormalized axial density. The non-perturbative calculation
of O(a) correction terms (as they appear in Symanzik's improvement programme)
is another important field of application.


title: Testing the heating method with perturbation theory

abstract:
  The renormalization constants present in the lattice evaluation of the
topological susceptibility can be non-perturbatively calculated by using the
so-called heating method. We test this method for the $O(3)$ non-linear
$\sigma$-model in two dimensions. We work in a regime where perturbative
calculations are exact and useful to check the values obtained from the heating
method. The result of the test is positive and it clarifies some features
concerning the method. Our procedure also allows a rather accurate
determination of the first perturbative coefficients.


title: Chiral Symmetry Restoration and $Z_N$ Symmetry

abstract:
  We demonstrate that chiral symmetry restoration in quenched finite
temperature QCD depends crucially on the $Z_3$ phase of the Polyakov loop
${\cal P}$. This dependence is a general consequence of the coupling of the
chiral order parameter to the Polyakov loop. We construct a model for chiral
symmetry breaking and restoration which includes the effect of a nontrivial
Polyakov loop by calculating the effective potential for the chiral condensate
of a Nambu-Jona-Lasinio model in a uniform temperature dependent $A_0$ gauge
field background. Above the deconfinement temperature there are three possible
phases corresponding to the $Z_3$ symmetric phases of the Polyakov loop in the
pure gauge theory. In the phase in which ${\rm tr_c}({\cal P})$ is real and
positive the first order deconfining transition induces chiral symmetry
restoration in agreement with simulation results. In the two phases where
$Re[{\rm tr_c}({\cal P})] < 0$ the sign of the leading finite temperature
correction to the effective potential is reversed from the normal phase, and
chiral symmetry is not restored at the deconfinement transition; this agrees
with the recent simulation studies of Chandrasekharan and Christ. In the case
of $SU(N)$ a rich set of possibilites emerges. The generality of the mechanism
makes it likely to occur in full QCD as well; this will increase the lifetimes
of metastable $Z_3$ phases.


title: Singular Vertices and the Triangulation Space of the D-sphere

abstract:
  By a sequence of numerical experiments we demonstrate that generic
triangulations of the $D-$sphere for $D>3$ contain one {\it singular}
$(D-3)-$simplex. The mean number of elementary $D-$simplices sharing this
simplex increases with the volume of the triangulation according to a simple
power law. The lower dimension subsimplices associated with this
$(D-3)-$simplex also show a singular behaviour. Possible consequences for the
DT model of four-dimensional quantum gravity are discussed.


title: Monte Carlo Simulation of the Three Dimensional Thirring Model

abstract:
  We study the Thirring model in three spacetime dimensions, by means of Monte
Carlo simulation on lattice sizes 8^3 and 12^3, for numbers of fermion flavors
N_f=2,4,6. For sufficiently strong interaction strength, we find that
spontaneous chiral symmetry breaking occurs for N_f=2,4, in accordance with the
predictions of the Schwinger-Dyson approach. The phase transitions which occur
are continuous and with critical scaling behaviour depending on N_f. For N_f=6
our results are preliminary, and no firm conclusions about the existence or
otherwise of chiral symmetry breaking are possible


title: The Complex Structure of 2D Surfaces

abstract:
  The complex structure of a surface generated by the two-dimensional dynamical
triangulation(DT) is determined by measuring the resistivity of the surface. It
is found that surfaces coupled to matter fields have well-defined complex
structures for cases when the matter central charges are less than or equal to
one, while they become unstable beyond c=1. A natural conjecture that fine
planar random network of resistors behave as a continuous sheet of constant
resistivity is justified numerically for c<1.


title: More On The SU(2) Deconfinement Transition In The Mixed Action

abstract:
  We examine certain issues related to the universality of the SU(2) lattice
gauge theory at non-zero temperatures. Using Monte Carlo simulations and strong
coupling expansions, we study the behavior of the deconfinement transition in
an extended coupling plane (beta, beta_A) around the tricritical point where
the deconfinement transition changes from second to first order. Our numerical
results on N_tau =2,4,6,8 lattices show that the tricritical point first moves
down towards the Wilson axis and and then moves slowly upwards, if at all, as
the lattice spacing is reduced. Lattices with very large N_tau seem to be
therefore necessary for the mixed action to exhibit the critical exponents of
the three dimensional Ising model for positive values of the adjoint coupling.


title: Phases and fractal structures of three-dimensional simplicial gravity

abstract:
  We study phases and fractal structures of three-dimensional simplicial
quantum gravity by the Monte-Carlo method. After measuring the surface area
distribution (SAD) which is the three-dimensional analog of the loop length
distribution (LLD) in two-dimensional quantum gravity, we classify the fractal
structures into three types: (i) in the hot (strong coupling) phase, strong
gravity makes the space-time one crumpled mother universe with small
fluctuating branches around it. This is a crumpled phase with a large Hausdorff
dimension $d_{\mbox{\tiny H}} \simeq 5$. The topologies of cross-sections are
extremely complicated. (ii) at the critical point, we observe that the
space-time is a fractal-like manifold which has one mother universe with small
and middle size branches around it. The Hausdorff dimension is $d_{\mbox{\tiny
H}} \simeq 4$. We observe some scaling behaviors for the cross-sections of the
manifold. This manifold resembles the fractal surface observed in
two-dimensional quantum gravity. (iii) in the cold (weak coupling) phase, the
mother universe disappears completely and the space-time seems to be the
branched-polymer with a small Hausdorff dimension $d_{\mbox{\tiny H}} \simeq
2$. Almost all of the cross-sections have the spherical topology $S^2$ in the
cold phase.


title: Two-Dimensional Seven-State Potts Model Under External Magnetic Field

abstract:
  The two-dimensional Potts Model with seven states under external field is
studied using a cluster algorithm. Cluster size distribution and the
fluctuations in the average cluster size provide helpful information on the
order of phase transitions.


title:
Performance Tests of the Kramers Equation and Boson Algorithms for
  Simulations of QCD

abstract:
  We present a performance comparison of the Kramers equation and the boson
algorithms for simulations of QCD with two flavors of dynamical Wilson fermions
and gauge group $SU(2)$. Results are obtained on $6^312$, $8^312$ and $16^4$
lattices. In both algorithms a number of optimizations are installed.


title: The Standard Model from a New Phase Transition on the Lattice

abstract:
  Several years ago it was conjectured in the so-called Roma Approach, that
gauge fixing is an essential ingredient in the lattice formulation of chiral
gauge theories. In this paper we discuss in detail how the gauge-fixing
approach may be realized. As in the usual (gauge invariant) lattice
formulation, the continuum limit corresponds to a gaussian fixed point, that
now controls both the transversal and the longitudinal modes of the gauge
field. A key role is played by a new phase transition separating a conventional
Higgs or Higgs-confinement phase, from a phase with broken rotational
invariance. In the continuum limit we expect to find a scaling region, where
the lattice correlators reproduce the euclidean correlation functions of the
target (chiral) gauge theory, in the corresponding continuum gauge.


title: Hyper-Systolic Processing on APE100/Quadrics: N^2-Loop Computations

abstract:
  We investigate the performance gains from hyper-systolic implementations of
n^2-loop problems on the massively parallel computer Quadrics, exploiting its
3-dimensional interprocessor connectivity. For illustration we study the
communication aspects of an exact molecular dynamics simulation of n particles
with Coulomb (or gravitational) interactions. We compare the interprocessor
communication costs of the standard-systolic and the hyper-systolic approaches
for various granularities. We predict gain factors as large as 3 on the Q4 and
8 on the QH4 and measure actual performances on these machine configurations.
We conclude that it appears feasable to investigate the thermodynamics of a
full gravitating n-body problem with O(10000) particles using the new method on
a QH4 system.


title: Hadron Spectrum with Wilson fermions

abstract:
  We present results of a high statistics study of the quenched spectrum using
Wilson fermions at $\beta=6.0$ on $32^3 \times 64$ lattices. We calculate the
masses of mesons and baryons composed of both degenerate and non-degenerate
quarks. Using non-degenerate quark combinations allows us to study baryon mass
splittings in detail. We find significant deviations from the lowest order
chiral expansion, deviations that are consistent with the expectations of
quenched chiral perturbation theory. We find that there is a $\sim 20%$
systematic error in the extracted value of $m_s$, depending on the meson mass
ratio used to set its value. Using the largest estimate of $m_s$ we find that
the extrapolated octet mass-splittings are in agreement with the experimental
values, as is $M_\Delta - M_N$, while the decuplet splittings are 30% smaller
than experiment. Combining our results with data from the GF11 collaboration we
find considerable ambiguity in the extrapolation to the continuum limit. Our
preferred values are $M_N / M_\rho = 1.38(7)$ and $M_\Delta / M_\rho =
1.73(10)$, suggesting that the quenched approximation is good to only $\sim
10-15%$. We also analyze the $O(ma)$ discretization errors in heavy quark
masses.


title:
$3$--Dimensional Approach to Hot Electroweak Matter for $M_{Higgs} \leq
  70$ GeV

abstract:
  We study the electroweak phase transition by lattice simulations of an
effective 3-dimensional theory, for a Higgs mass of about $70$ GeV. Exploiting
a variant of the equal weight criterion of phase equilibrium, we obtain
transition temperature, latent heat and surface tension and compare with $M_H
\approx 35$ GeV. For the symmetric phase, bound state masses and the static
force are determined and compared with results for pure $SU(2)$ theory.


title: Perspectives in Lattice Gravity

abstract:
  We briefly overview the development of Euclidean quantum gravity in four
dimensions regarded as a branch of statistical mechanics of discretized random
manifolds.


title:
Evidence of Strong Correlation between Instanton and QCD-monopole on
  SU(2) Lattice

abstract:
  The correlation between instantons and QCD-monopoles is studied both in the
lattice gauge theory and in the continuum theory. An analytical study in the
Polyakov-like gauge, where $A_4(x)$ is diagonalized, shows that the
QCD-monopole trajectory penetrates the center of each instanton, and becomes
complicated in the multi-instanton system. Using the SU(2) lattice with $16^4$,
the instanton number is measured in the singular (monopole-dominating) and
regular (photon-dominating) parts, respectively. The monopole dominance for the
topological charge is found both in the maximally abelian gauge and in the
Polyakov gauge.


title: The Heavy-Light Spectrum from Lattice NRQCD

abstract:
  We present a lattice investigation of heavy-light mesons in the quenched
approximation, using non-relativistic QCD for the heavy quark and a clover
improved Wilson formulation for the light quark. A comprehensive calculation of
the heavy-light spectrum has been performed for various heavy quark masses
around the $b$. Our results for the $B_s-B_d$ splitting agree well with the
experimental value. We find the $\Lambda_b-B$ splitting to be compatible with
experiment, albeit with large error bars. Our $B^*-B$ splitting is slightly
low, which could be explained as an effect of quenching. For the first time, we
are able to estimate the mass of $P$ states at the $B$ and compare them with
experiment.


title:
Upsilon and J/Psi Spectroscopy Using Clover Fermions in the Presence of
  Dynamical Quarks

abstract:
  We calculate spin averaged splittings in the bottomonium and charmonium
systems using the clover action. We compare static and kinetic masses of
heavy-heavy and heavy-light mesons and discuss the consistency of the results.


title:
A Comparison of Clover and Wilson Spectroscopy in the Presence of
  Dynamical Quarks

abstract:
  We present preliminary results of light hadron spectroscopy using valence,
tadpole-improved, Clover fermions on an ensemble of gauge configurations
generated with 2 flavors of staggered fermions at a beta of 5.6. We compare the
slope and intercept of the curve M_V vs. M_PS^2 for Clover and Wilson fermions.
We show that a higher order chiral perturbation theory ansatz works very well
for chiral extrapolations.


title: On the Definition of the Partition Function in Quantum Regge Calculus

abstract:
  We argue that the definition of the partition function used recently to
demonstrate the failure of Regge calculus is wrong. In fact, in the
one-dimensional case, we show that there is a more natural definition, with
which one can reproduce the correct results.


title: Lattice Regularized QCD at Finite Temperature

abstract:
  During the first part of this review we will focus on the thermodynamics of
$SU(N)$ gauge theories at finite temperature. We will present results from a
calculation of electric and magnetic screening masses for the gluons, discuss
calculations of the critical temperature in units of the string tension and
bulk thermodynamic quantities like the energy density and pressure. In
particular, the latter calculations have now reached a stage where $O(a^2)$
cut-off effects can be controlled systematically and an extrapolation to the
continuum limit can be performed. In the second part we discuss the critical
behaviour of QCD with light quarks. We analyze the chiral transition in
2-flavour QCD and present results on the temperature dependence of hadron
properties.


title: Monopole Order Parameter in SU(2) Lattice Gauge Theory

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


title:
Hadron Masses and Decay Constants with Wilson Quarks at $\beta=5.85$ and
  6.0

abstract:
  We present results of a high statistics calculation of hadron masses and
meson decay constants in the quenched approximation to lattice QCD with Wilson
quarks at $\beta=$ 5.85 and 6.0 on $24^3 \times 54$ lattices. We analyze the
data paying attention in particular to the systematic errors due to the choice
of fitting range and due to the contamination from excited states. We find that
the systematic errors for the hadron masses with quarks lighter than the
strange quark amount to 1 --- 2 times the statistical errors. When the lattice
scale is fixed from the $\rho$ meson mass, the masses of the $\Omega^{-}$
baryon and the $\phi$ meson at two $\beta$'s agree with experiment within about
one standard deviation. On the other hand, the central value of the nucleon
mass at $\beta=6.0$ (5.85) is larger than its experimental value by about 15\%
(20\%) and that of the $\Delta$ mass by about 15\% (4\%): Even when the
systematic errors are included, the baryon masses at $\beta=6.0$ do not agree
with experiment. Vector meson decay constants at two values of $\beta$ agree
well with each other and are consistent with experiment for a wide range of the
quark mass, when we use current renormalization constants determined
nonperturbatively by numerical simulations. The pion decay constant agrees with
experiment albeit with large errors. Results for the masses of excited states
of the $\rho$ meson and the nucleon are also presented.


title: Fixed Point Action and Topology in the CP^3 Model

abstract:
  We define a fixed point action in two-dimensional lattice ${\rm CP}^{N-1}$
models. The fixed point action is a classical perfect lattice action, which is
expected to show strongly reduced cutoff effects in numerical simulations.
Furthermore, the action has scale-invariant instanton solutions, which enables
us to define a correct topological charge without topological defects. Using a
parametrization of the fixed point action for the ${\rm CP}^{3}$ model in a
Monte Carlo simulation, we study the topological susceptibility.


title:
Chiral symmetry at finite T, the phase of the Polyakov loop and the
  spectrum of the Dirac operator

abstract:
  A recent Monte Carlo study of {\em quenched} QCD showed that the chiral
condensate is non-vanishing above $T_c$ in the phase where the average of the
Polyakov loop $P$ is complex. We show how this is related to the dependence of
the spectrum of the Dirac operator on the boundary conditions in Euclidean
time. We use a random matrix model to calculate the density of small
eigenvalues and the chiral condensate as a function of $\arg P$. The chiral
symmetry is restored in the $\arg P=2\pi/3$ phase at a higher $T$ than in the
$\arg P=0$ phase. In the phase $\arg P = \pi$ of the $SU(2)$ gauge theory the
chiral condensate stays nonzero for all~$T$.


title: Order parameters and boundary effects in U(1) lattice gauge theory

abstract:
  We show that, independently of the boundary conditions, the two phases of the
4-dimensional compact U(1) lattice gauge theory can be characterized by the
presence or absence of an ``infinite'' current network, with an appropriate
definition of ``infinite'' for the various types of boundary conditions imposed
on the finite lattice. The probability for the occurrence of an ``infinite''
network takes values 0 or 1 in the cold and hot phase, respectively. It thus
constitutes a very efficient order parameter, which allows one to determine the
transition region at low computational cost. In addition, for open and fixed
boundary conditions we address the question of the impact of inhomogeneities
and give examples of the reappearance of an energy gap already at moderate
lattice sizes.


title: Period of K System Generator of Pseudorandom Numbers

abstract:
  We analyze the structure of the periodic trajectories of the matrix generator
of pseudorandom numbers which has been proposed earlier. The structure of the
periodic trajectories becomes more transparent when the rational sublattice
coincides with the Galois field $GF[p]$. We are able to compute the period of
the trajectories as a function of $p$ and the dimension of the matrix $d$.


title: A multisite microcanonical updating method

abstract:
  We have made a study of several update algorithms using the XY model. We find
that sequential local overrelaxation is not ergodic at the scale of typical
Monte Carlo simulation time. We have introduced a new multisite microcanonical
update method, which yields results compatible with those of random
overrelaxation and the microcanonical demon algorithm, which are very much
slower, all being incompatible with the sequential overrelaxation results.


title: M.C.R.G. Study of Fixed-connectivity Surfaces

abstract:
  We apply Monte Carlo Renormalization group to the crumpling transition in
random surface models of fixed connectivity. This transition is notoriously
difficult to treat numerically. We employ here a Fourier accelerated Langevin
algorithm in conjunction with a novel blocking procedure in momentum space
which has proven extremely successful in $\lambda\phi^4$. We perform two
successive renormalizations in lattices with up to $64^2$ sites. We obtain a
result for the critical exponent $\nu$ in general agreement with previous
estimates and similar error bars, but with much less computational effort. We
also measure with great accuracy $\eta$. As a by-product we are able to
determine the fractal dimension $d_H$ of random surfaces at the crumpling
transition.


title: Lipatov Pomeron and the Heisenberg chain

abstract:
  It is pointed out that the recently discovered analogy between the QCD
description of the Pomeron exchange and the Heisenberg chain may allow to apply
lattice techniques to the high energy phenomena.


title: The Status of Lattice Calculations of the Nucleon Structure Functions

abstract:
  We review our progress on the lattice calculation of low moments of both the
unpolarised and polarised nucleon structure functions.


title: Desperately Seeking Chiral Fermions

abstract:
  Chiral fermions can (presumably) be constructed by introducing two
regulators, one for the gauge fields (e.g. a lattice), and another for the
fermion functional integrals in a fixed (regulated) gauge field. This talk
discusses cutoff effects arising from the regulator of the fermions.


title: Recent results in high temperature lattice gauge theories

abstract:
  We review some analytic results on the deconfinement transition in pure
lattice gauge theories. In particular we discuss the relationship between the
deconfinement transition in the $(d+1)$-dimensional $SU(2)$ model and the
magnetization transition in the $d$-dimensional Ising model. This analysis
leads to a precise estimate of the deconfinement temperature which agrees well
with that obtained with a Montecarlo simulation in the case in which the
lattice has only one link in the compactified time direction.


title:
The Lattice Schrodinger Functional and the Background Field Effective
  Action

abstract:
  We propose a new method that by using the lattice Schr\"odinger functional
allows to investigate the effective action for external background fields in
lattice gauge theories. We show that this method gives sensible results for the
case of four-dimensional U(1) gauge theory in an external constant magnetic
field.


title: The Roughening Transition of the 3D Ising Interface: A Monte Carlo Study

abstract:
  We study the roughening transition of an interface in an Ising system on a 3D
simple cubic lattice using a finite size scaling method. The particular method
has recently been proposed and successfully tested for various solid on solid
models. The basic idea is the matching of the renormalization-group-flow of the
interface with that of the exactly solvable body centered cubic solid on solid
model. We unambiguously confirm the Kosterlitz-Thouless nature of the
roughening transition of the Ising interface. Our result for the inverse
transition temperature $K_R=0.40754(5)$ is almost by two orders of magnitude
more accurate than the estimate of Mon, Landau and Stauffer.


title: Large q expansion of the 2D q-states Potts model

abstract:
  We present a recursive method to calculate a large q expansion of the 2d
q-states Potts model free energies based on the Fortuin-Kasteleyn
representation of the model. With this procedure, we compute directly the
ordered phase partition function up to order 10 in 1/sqrt{q}. The energy
cumulants at the transition can be obtained with suitable resummation and come
out large for q less or around 15. As a consequence, expansions of the free
energies around the transition temperature are useless for not large enough
values of q. In particular the pure phase specific heats are predicted to be
much larger, at q < 15, than the values extracted from current finite size
scaling analysis of extrema, whereas they agree very well with recent values
extracted at the transition point.


title: Abelian dominance and adjoint sources in lattice QCD

abstract:
  Certain properties of maximal abelian projection are derived which suggest
that the fundamental and adjoint SU(2) string tensions are reproduced by singly
and doubly charged abelian Wilson loops, respectively. Thus, abelian dominance,
which has been observed for color sources (quarks) in the fundamental
representation, can be extended to higher representations. Numerical evidence
in support of this conjecture also for adjoint quarks is presented. The
difference between maximal abelian and local projections is elucidated and the
role of non-Wilson-like terms in the effective abelian action is discussed.


title: Iterating Block Spin Transformations of the O(3) Non-Linear Sigma-Model

abstract:
  We study the iteration of block spin transformations in the O(3) symmetric
non-linear sigma-model on a two-dimensional square lattice with help of the
Monte Carlo method. In contrast to the classical Monte Carlo Renormalization
Group approach, we do attempt to explicitly compute the block spin effective
actions. Using two different methods for the determination of effective
couplings, we study the renormalization group flow for various parametrization
and truncation schemes. The largest ansatz for the effective action contains
thirteen coupling constants.
  Actions on the renormalized trajectory should describe theories with no
lattice artefacts, even at small correlation length. However, tests with the
step scaling function of Luescher et al. reveal that our truncated effective
actions show sizable scaling violations indicating that the ansaetze are still
too small.


title:
A microscopic semiclassical confining field equation for $U(1)$ lattice
  gauge theory in 2+1 dimensions

abstract:
  We present a semiclassical nonlinear field equation for the confining field
in 2+1--dimensional $U(1)$ lattice gauge theory (compact QED). The equation is
derived directly from the underlying microscopic quantum Hamiltonian by means
of truncation. Its nonlinearities express the dynamic creation of magnetic
monopole currents leading to the confinement of the electric field between two
static electric charges. We solve the equation numerically and show that it can
be interpreted as a London relation in a dual superconductor.


title:
Numerical tests of the electroweak phase transition and thermodynamics
  of the electroweak plasma

abstract:
  The finite temperature phase transition in the SU(2) Higgs model at a Higgs
boson mass $M_H \simeq 34$ GeV is studied in numerical simulations on
four-dimensional lattices with time-like extensions up to $L_t=5$. The effects
of the finite volume and finite lattice spacing on masses and couplings are
studied in detail. The errors due to uncertainties in the critical hopping
parameter are estimated. The thermodynamics of the electroweak plasma near the
phase transition is investigated by determining the relation between energy
density and pressure.


title: Semileptonic Decays: an Update Down Under

abstract:
  Heavy-meson semileptonic decays calculations on the lattice are reviewed. The
focus is upon obtaining reliable matrix elements. Errors that depend upon the
lattice spacing, $a$, are an important source of systematic error. Full $O(a)$
improvement of matrix elements for arbitrary-mass four-component quarks is
discussed. With improvement, bottom-quark matrix elements can be calculated
directly using current lattices. Momentum dependent errors for $O(a)$-improved
quarks and statistical noise limit momenta to around 1 GeV/c with current
lattices. Hence, maximum recoil momenta can be reached for $D$ decays while
only a fraction of the maximum recoil momentum can be reliably studied for the
light-meson decay modes of the $B$. Differential decay rates and partial widths
are phenomenologically important quantities in $B$ decays that can be reliably
determined with present lattices.


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

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


title:
Confinement by Monopoles in the Positive Plaquette Model of SU(2)
  Lattice Gauge Theory

abstract:
  Confinement via 't Hooft-Mandelstam monopoles is studied for the positive
plaquette model in SU(2) lattice gauge theory. Positive plaquette model
configurations are projected into the maximum abelian gauge and the magnetic
current extracted. The resulting magnetic current is used to compute monopole
contributions to Wilson loops and extract a monopole contribution to the string
tension. As was previously found for the Wilson action, the monopole
contribution to the string tension agrees with the string tension calculated
directly from the SU(2) links. The fact that the positive plaquette model
suppresses Z2 monopoles and vortices is discussed.


title:
Toward an analytic determination of the deconfinement temperature in
  SU(2) L.G.T.

abstract:
  We consider the SU(2) lattice gauge theory at finite temperature in (d+1)
dimensions, with different couplings $\beta_t$ and $\beta_s$ for timelike and
spacelike plaquettes. By using the character expansion of the Wilson action and
performing the integrals over space-like link variables, we find an effective
action for the Polyakov loops which is exact to all orders in $\beta_t$ and to
the first non-trivial order in $\beta_s$. The critical coupling for the
deconfinement transition is determined in the (3+1) dimensional case, by the
mean field method, for different values of the lattice size $N_t$ in the
compactified time direction and of the asymmetry parameter $\rho =
\sqrt{\beta_t/\beta_s}$. We find good agreement with Montecarlo simulations in
the range $1\leq N_t \leq 5$, and good qualitative agreement in the same range
with the logarithmic scaling law of QCD. Moreover the dependence of the results
from the parameter $\rho$ is in excellent agreement with previous theoretical
predictions.


title:
Effective Potential for Scalar Field in Three Dimensions: Ising Model in
  the Ferromagnetic Phase

abstract:
  We compute the effective potential $V_{\rm eff}(\phi)$ for one-component real
scalar field $\phi$ in three Euclidean dimensions (3D) in the case of
spontaneously broken symmetry, from the Monte Carlo simulation of the 3D Ising
model in external field at temperatures approaching the phase transition from
below. We study probability distributions of the order parameter on the
lattices from $30^3$ to $74^3$, at $L/\xi \approx 10$. We find that, in close
analogy with the symmetric case, $\phi^6$ plays an important role: $V_{\rm
eff}(\phi)$ is very well approximated by the sum of $\phi^2$, $\phi^4$ and
$\phi^6$ terms. An unexpected feature is the negative sign of the $\phi^4$
term. As close to the continuum limit as we can get ($\xi \approx 7.2$), we
obtain
  $$ {\cal L}_{\rm eff} \approx
  {1 \over 2} \partial_\mu \phi \partial_\mu \phi +
  1.7 (\phi^2 - \eta^2)^2 (\phi^2 + \eta^2). $$
  We also compute several universal coupling constants and ratios, including
the combination of critical amplitudes $C^- (f_1^-)^{-3} B^{-2}$.


title: Heavy Baryon Specroscopy from the Lattice

abstract:
  The results of an exploratory lattice study of heavy baryon spectroscopy are
presented. We have computed the full spectrum of the eight baryons containing a
single heavy quark, on a $24^3\times 48$ lattice at $\beta=6.2$, using an
$O(a)$-improved fermion action. We discuss the lattice baryon operators and
give a method for isolating the contributions of the spin doublets
$(\Sigma,\Sigma^*)$, $(\Xi',\Xi^*)$ and $(\Omega,\Omega^*)$ to the correlation
function of the relevant operator. We compare our results with the available
experimental data and find good agreement in both the charm and the beauty
sectors, despite the long extrapolation in the heavy quark mass needed in the
latter case. We also predict the masses of several undiscovered baryons. We
compute the $\Lambda-\mbox{pseudoscalar meson}$ and $\Sigma-\Lambda$ mass
splittings. Our results, which have errors in the range $ 10-30\%$, are in good
agreement with the experimental numbers. For the $\Sigma^*-\Sigma$ mass
splitting, we find results considerably smaller than the experimental values
for both the charm and the beauty baryons, although in the latter case the
experimental results are still preliminary. This is also the case for the
lattice results for the hyperfine splitting for the heavy mesons.


title:
Mean Field Phase Diagram of SU(2)xSU(2) Lattice Higgs-Yukawa Model at
  Finite Lambda

abstract:
  The phase diagram of an SU(2)_L x SU(2)_R lattice Higgs-Yukawa model with
finite lambda is constructed using mean field theory. The phase diagram bears a
superficial resemblance to that for infinite lambda, however as lambda is
decreased the paramagnetic region shrinks in size. For small lambda the phase
transitions remain second order, and no new first order transitions are seen.


title: Focusing on the Fixed Point of 4D Simplicial Gravity

abstract:
  Our earlier renormalization group analysis of simplicial gravity is extended.
A high statistics study of the volume and coupling constant dependence of the
cumulants of the node distribution is carried out. It appears that the phase
transition of the theory is of first order, contrary to what is generally
believed.


title: Testing logarithmic violations to scaling in strongly coupled QED

abstract:
  Using very precise measurements of the critical couplings for the chiral
transition of non compact $QED_4$ with up to 8 flavours, we analyse the
behaviour of the order parameter at the critical point using the equation of
state of a logarithmically improved scalar mean field theory, that of the
Nambu-Jona Lasinio theory and a pure power law. The first case is definitively
excluded by the numerical data. The stability of the fits for the last two
cases, as well as the behaviour with the number of flavours of the exponent of
the logarithmic violations to the scaling favour clearly a pure power law
scaling with non mean field exponents.


title:
Chiral Susceptibilities in noncompact QED: a new determination of the
  $\gamma$ exponent and the critical couplings

abstract:
  We report the results of a measurement of susceptibilities in noncompact
$QED_4$ in $8^4, 10^4$ and $12^4$ lattices. Due to the potentialities of the
$MFA$ approach, we have done simulations in the chiral limit which are
therefore free from arbitrary mass extrapolations. Our results in the Coulomb
phase show unambiguously that the susceptibility critical exponent $\gamma=1$
independently of the flavour symmetry group. The critical couplings extracted
from these calculations are in perfect agreement with previous determinations
based on the fermion effective action and plaquette energy, and outside the
predictions of a logarithmically improved scalar mean field theory by eight
standard deviations.


title:
The gauged Nambu - Jona Lasinio model: a mean field calculation with non
  mean field exponents

abstract:
  We analyse the phase diagram of the lattice gauged Nambu-Jona Lasinio model
with the help of a mean field approximation plus numerical simulations. We find
a phase transition line in the coupling parameters space separating the
chirally broken phase from the symmetric phase, which is in good qualitative
agreement with results obtained in the quenched-ladder approximation. The mean
field approximation relates the critical exponents along the continuous phase
transition line with the mass dependence of the chiral condensate in the
Coulomb phase of standard noncompact $QED$. Our numerical results for
noncompact $QED$ strongly suggest non mean field exponents along the critical
line.


title: The Continuum Limit of Non Compact QED

abstract:
  Since four-fermion operators in strongly coupled $QED$ are nonperturbatively
renormalizable, we analyze here the phase diagram and critical behaviour of the
Gauged Nambu-Jona Lasinio model. Our mean field approximation relates the
critical exponents along the continuous phase transition line with the mass
dependence of the chiral condensate in the Coulomb phase of standard noncompact
$QED$. The numerical results for noncompact $QED$ strongly suggest non mean
field exponents along the critical line.


title: The Kosterlitz-Thouless Universality Class

abstract:
  We examine the Kosterlitz-Thouless universality class and show that essential
scaling at this type of phase transition is not self-consistent unless
multiplicative logarithmic corrections are included. In the case of specific
heat these logarithmic corrections are identified analytically. To identify
those corresponding to the susceptibility we set up a numerical method
involving the finite-size scaling of Lee-Yang zeroes. We also study the density
of zeroes and introduce a new concept called index scaling. We apply the method
to the XY-model and the closely related step model in two dimensions. The
critical parameters (including logarithmic corrections) of the step model are
compatable with those of the XY-model indicating that both models belong to the
same universality class. This result then raises questions over how a vortex
binding scenario can be the driving mechanism for the phase transition.
Furthermore, the logarithmic corrections identified numerically by our methods
of fitting are not in agreement with the renormalization group predictions of
Kosterlitz and Thouless.


title: Finite Temperature Spacelike Gluon Propagators in Lattice Momentum Space

abstract:
  We study the behaviour of lattice momentum-space gluon propagators for a pure
$SU(2)$ gauge theory at finite temperature. We find out that the magnetic mass
is $0.26 g^2(T) T$; we have repeated the same calculations in three dimensions.


title:
Phase structure and confinement properties of noncompact gauge theories
  II. Z(N) Wilson loop and effective noncompact model

abstract:
  An approach to studying lattice gauge models in the weak coupling region is
proposed. Conceptually, it is based on the crucial role of the original Z(N)
symmetry and the invariant gauge group measure. As an example, we calculate an
effective model from the compact Wilson formulation of the SU(2) gauge theory
in $d=3D3$ dimensions at zero temperature. Confining properties and phase
structure of the effective model are studied in details.


title:
The Continuum Limit of One-Dimensional Quantum Regge Calculus with
  Massive Bosons

abstract:
  The most essential problems in Regge calculus discretization are the
definitions of the partition function and the integral measure for
link--length. In recent work, by considering the one--dimensional case, it was
suggested that we should define the partition function in a certain form. But
in that work, the model which authors used was over simplified hence the
conclusions may be unreliable. To confirm their claim, we consider a case that
is more realistic.


title: Anti-Ferromagnetic Condensate in Yang-Mills Theory

abstract:
  SU(2) gauge theory with competing interactions is shown to possess a rich
phase structure with anti-ferromagnetic vacua. It is argued that the phase
boundaries persist in the weak coupling limit suggesting the existence of
different renormalized continuum theories for QCD.


title:
Renormalization of the Classical Velocity in the Lattice Heavy Quark
  Effective Theory

abstract:
  In the lattice formulation of the Heavy Quark Effective Theory (LHQET), the
classical velocity becomes renormalized. The origin of this renormalization is
the reduction of Lorentz (or O(4)) invariance to (hyper)cubic invariance. The
renormalization is finite, depends on the form of the discretization of the
reduced heavy quark Dirac equation, and can persist down to zero lattice
spacing. 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
ACP-MAPS collaboration. The estimates of the leading multiplicative shift agree
reasonably well, and indicate that to first order, the classical velocity is
reduced by about 20-25%.


title: Electromagnetic Splittings and Light Quark Masses in Lattice QCD

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


title: On the Mass Spectrum of the SU(2) Higgs Model in 2+1 Dimensions

abstract:
  We calculate the masses of the low-lying states with quantum numbers
$J^{PC}=0^{++},1^{--}$ in the Higgs and confinement regions of the
three-dimensional SU(2) Higgs model, which plays an important r\^ole in the
description of the thermodynamic properties of the standard model at finite
temperatures. We extract the masses from correlation functions of
gauge-invariant operators which are calculated by means of a lattice Monte
Carlo simulation. The projection properties of our lattice operators onto the
lowest states are greatly improved by the use of smearing techniques. We also
consider cross correlations between various operators with the same quantum
numbers. From these the mass eigenstates are determined by means of a
variational calculation. In the symmetric phase, we find that some of the
ground state masses are about 30\% lighter than those reported from previous
simulations. We also obtain the masses of the first few excited states in the
symmetric phase. Remarkable among these is the occurrence of a $0^{++}$ state
composed almost entirely of gauge degrees of freedom. The mass of this state,
as well as that of its first excitations, is nearly identical to the
corresponding glueball states in three-dimensional SU(2) pure gauge theory,
indicating an approximate decoupling of the pure gauge sector from the Higgs
sector of the model. We perform a detailed study of finite size effects and
extrapolate the lattice mass spectrum to the continuum.


title: Thermodynamics of SU(3) Lattice Gauge Theory

abstract:
  The pressure and the energy density of the $SU(3)$ gauge theory are
calculated on lattices with temporal extent $N_\tau = 4$, 6 and 8 and spatial
extent $N_\sigma =16$ and 32. The results are then extrapolated to the
continuum limit. In the investigated temperature range up to five times $T_c$
we observe a $15\%$ deviation from the ideal gas limit. We also present new
results for the critical temperature on lattices with temporal extent $N_\tau =
8$ and 12. At the corresponding critical couplings the string tension is
calculated on $32^4$ lattices to fix the temperature scale. An extrapolation to
the continuum limit yields $T_c/\sqrt{\sigma} = 0.629(3)$. We furthermore
present results on the electric and magnetic condensates as well as the
temperature dependence of the spatial string tension. These observables suggest
that the temperature dependent running coupling remains large even at $T\simeq
5T_c$. For the spatial string tension we find $\sqrt{\sigma_s}/T = 0.566(13)
g^2(T)$ with $g^2(5T_c) \simeq 1.5$.


title:
A General Implicit Splitting for Stabilizing Numerical Simulations of
  Langevin Equations

abstract:
  In this paper is described a general 2-nd order accurate (weak sense)
procedure for stablizing Monte-Carlo simulations of Ito stochastic differential
equations. The splitting procedure includes explicit Runge-Kutta methods,
semi-implicit methods, and trapezoidal Rule. We prove the semi-implicit method
of Oettinger and note that it may be generalized for arbitrary splittings.


title: 2D Lorentzian Gravity as 2D Euclidean Gravity with Ising Spins

abstract:
  We suggest a generalization of the dynamical triangulation approach to
quantum gravity with both timelike and spacelike edges, which can serve as a
toy model for quantum gravity in the Lorentz sector in two dimensions. It is
possible to consider the model in a purely Lorentzian sector or to relax this
constraint and allow local signature changing moves. We show that, with
suitable conventions, the model is equivalent to an Ising model coupled to 2D
Euclidean quantum gravity and conduct a preliminary numerical simulation of the
Lorentz sector.


title: QCD $\beta$ Function with Two Flavors of Dynamical Wilson Fermions

abstract:
  We test the asymptotic scaling behavior of state-of-the-art simulations of
QCD with two flavors of light Wilson fermions. This is done by matching $\pi$
and $\rho$ masses on lattices of size $16^3\times32$ and $8^3\times16$. We find
that at $\beta=6/g^2=5.3$ matching is not possible over a range extending down
to $\beta=3.5$. The large lattice data at $\beta=5.5$ matches the small lattice
values at $\beta=4.9(1)$ leading to a shift $\Delta\beta=0.6(1)$, considerably
larger than the perturbative prediction of $0.45$. In both cases we conclude
that the simulations are very far from the asymptotic scaling region.


title:
A strong-coupling analysis of two-dimensional O(N) sigma models with
  $N\geq 3$ on square, triangular and honeycomb lattices

abstract:
  Recently-generated long strong-coupling series for the two-point Green's
functions of asymptotically free ${\rm O}(N)$ lattice $\sigma$ models are
analyzed, focusing on the evaluation of dimensionless renormalization-group
invariant ratios of physical quantities and applying resummation techniques to
series in the inverse temperature $\beta$ and in the energy $E$. Square,
triangular, and honeycomb lattices are considered, as a test of universality
and in order to estimate systematic errors. Large-$N$ solutions are carefully
studied in order to establish benchmarks for series coefficients and
resummations. Scaling and universality are verified. All invariant ratios
related to the large-distance properties of the two-point functions vary
monotonically with $N$, departing from their large-$N$ values only by a few per
mille even down to $N=3$.


title: Miscellanies of $ K^0 - \bar{K}^0 $ mixing and $ B_K $

abstract:
  We have computed $ B_K $, using two different methods with staggered fermions
on a $ 16^3 \times 40 $ lattice at $ \beta = 5.7 $ with two dynamical flavors
of a mass 0.01. % Using an improved wall source method, we have studied a
series of non-degenerate quark antiquark pairs and observed no effect on $ B_K
$, although effects were seen on the individual terms making up $ B_K $.


title:
Reply to Comment on ``Asymptotic Scaling in the Two-Dimensional O(3)
  sigma-Model at Correlation Length 10^5"

abstract:
  We reply to criticism by Patrascioiu and Seiler [hep-lat/9502019] of our
results [Phys. Rev. Lett. 75, 1891 (1995), hep-lat/9411009] on asymptotic
scaling in the two-dimensional $O(3)$ $\sigma$-model, which were based on a
finite-size-scaling extrapolation method.


title:
Self-consistent Calculation of Real Space Renormalization Group Flows
  and Effective Potentials

abstract:
  We show how to compute real space renormalization group flows in lattice
field theory by a self-consistent method. In each step, the integration over
the fluctuation field (high frequency components of the field) is performed by
a saddle point method. The saddle point depends on the block-spin. Higher
powers of derivatives of the field are neglected in the actions, but no
polynomial approximation in the field is made. The flow preserves a simple
parameterization of the action. In this paper we treat scalar field theories as
an example.


title:
Asymptotic scaling in the two-dimensional $SU(3)$ $\sigma$-model at
  correlation length $4 \times 10^5$

abstract:
  We carry out a high-precision simulation of the two-dimensional $SU(3)$
principal chiral model at correlation lengths $\xi$ up to $\approx\! 4 \times
10^5$, using a multi-grid Monte Carlo (MGMC) algorithm. We extrapolate the
finite-volume Monte Carlo data to infinite volume using finite-size-scaling
theory, and we discuss carefully the systematic and statistical errors in this
extrapolation. We then compare the extrapolated data to the
renormalization-group predictions. For $\xi \gtapprox 10^3$ we observe good
asymptotic scaling in the bare coupling; at $\xi \approx 4 \times 10^5$ the
nonperturbative constant is within 2--3\% of its predicted limiting value.


title: Non-hermitian Exact Local Bosonic Algorithm for Dynamical Quarks

abstract:
  We present an exact version of the local bosonic algorithm for the simulation
of dynamical quarks in lattice QCD. This version is based on a non-hermitian
polynomial approximation of the inverse of the quark matrix. A Metropolis test
corrects the systematic errors. Two variants of this test are presented. For
both of them, a formal proof is given that this Monte Carlo algorithm converges
to the right distribution. Simulation data are presented for different lattice
parameters. The dynamics of the algorithm and its scaling in lattice volume and
quark mass are investigated.


title: Interpolation of Non-abelian Lattice Gauge Fields

abstract:
  We propose a method for interpolating non-abelian lattice gauge fields to the
continuum, or to a finer lattice, which satisfies the properties of (i)
transverse continuity, (ii) (lattice) rotation and translation covariance,
(iii) gauge covariance, (iv) locality. These are the properties required for
use in our earlier proposal for non-perturbative formulation and simulation of
chiral gauge theories.


title:
Theoretical analysis of multi-boson algorithm with local and global
  update of bosonic fields

abstract:
  We estimate theoretically the cost of the multi-boson method in the
non-hermitian approximation. It is shown that it is proportional to $V(\log
V)^2/m^4$. For a global update of the scalar fields the cost decreases by a
factor $m$ with a $\log V$ overhead.


title: A Parallel SSOR Preconditioner for Lattice QCD

abstract:
  We present a parallelizable SSOR preconditioning scheme for Krylov subspace
iterative solvers which proves to be efficient in lattice QCD applications
involving Wilson fermions. Our preconditioner is based on a locally
lexicographic ordering of the lattice points. In actual hybrid Monte Carlo
applications with the bi-conjugate gradient stabilized method BiCGstab, we
achieve a gain factor of about 2 in the number of iterations compared to
conventional odd-even preconditioning. Whether this translates into similar
reductions in run time will depend on the parallel computer in use. We discuss
implementation issues using the `Eisenstat-trick' and machine specific
advantages of the method for the APE100/Quadrics parallel computer. In a full
QCD simulation with Wilson fermions on a 512-processor Quadrics QH4 we find a
gain in cpu-time of a factor of 1.7 over odd-even preconditioning for a 24^3 x
40 lattice.


title: $B_c$ Spectroscopy from Lattice QCD

abstract:
  We present first results for $B_c$ spectroscopy using Lattice
Non-Relativistic QCD (NRQCD). For the NRQCD action the leading order
spin-dependent and next to leading order spin-independent interactions have
been included with tadpole-improved coefficients. We use multi-exponential fits
to multiple correlation functions to extract ground and excited $S$ states and
give accurate values for the $S$ state hyperfine splitting and the P state
($B^{**}_c$) fine structure, including the effects of $^1P_1/^3P_1$ mixing.


title: RG flow in an exactly solvable model with fluctuating geometry

abstract:
  A recently proposed renormalization group technique, based on the
hierarchical structures present in theories with fluctuating geometry, is
implemented in the model of branched polymers. The renormalization group
equations can be solved analytically, and the flow in coupling constant space
can be determined.


title: Coupling Constants for Scalar Glueball Decay

abstract:
  We evaluate the partial decay widths of the lightest scalar glueball to pairs
of pseudoscalar quark-antiquark states. The calculation is done in the valence
(quenched) approximation on a $16^3 \time 24$ lattice at $\beta = 5.7$. These
predictions and values obtained earlier for the infinite volume continuum limit
of 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:
Universality in the Critical Behavior of the Correlation Functions in 2d
  Simplicial Gravity

abstract:
  The analogue of the loop-loop correlation function in 2d gravity for the
planar connected $\phi^3$ diagrams is calculated. It is shown that although the
discretized formulas are different the scaling limit is the same as for the
loop-loop correlation function. The derivation may serve as an alternative
definition of the volume-volume correlator of Euclidean quantum gravity in
$2d$.


title: $SU(2)$ gauge theory in the maximally abelian gauge without monopoles

abstract:
  We present an algorithm for simulation of $SU(2)$ lattice gauge theory under
the MA gauge and first numerical results for the theory without abelian
monopoles. The results support the idea that nonperturbative interaction arises
between monopoles and residual abelian field and the other interactions are
perturbative. It is shown that the Gribov region for the theory with the MA
gauge fixed is non-connected.


title: Universality of the Ising Model on Sphere-like Lattices

abstract:
  We study the 2D Ising model on three different types of lattices that are
topologically equivalent to spheres. The geometrical shapes are reminiscent of
the surface of a pillow, a 3D cube and a sphere, respectively. Systems of
volumes ranging up to O($10^5$) sites are simulated and finite size scaling is
analyzed. The partition function zeros and the values of various cumulants at
their respective peak positions are determined and they agree with the scaling
behavior expected from universality with the Onsager solution on the torus
($\nu=1$). For the pseudocritical values of the coupling we find significant
anomalies indicating a shift exponent $\neq 1$ for sphere-like lattice
topology.


title:
On the Universality of Certain Non-Renormalizable Contributions in
  Two-Dimensional Quantum Field Theory

abstract:
  We consider the question of removing the ultraviolet cutoff in a 2D Quantum
Field Theory with an interaction term which is non-renormalizable by power
counting. This model arises as the first non-trivial correction beyond the
Gaussian approximation of the so called Capillary Wave or Drumhead Model, and
is rather important from a physical point of view since it correctly describes
the finite size effects of two-dimensional interfaces. Despite the fact that
the interaction is non-renormalizable, we prove that for a large class of
regularization schemes the finite and divergent parts can be separated in a
simple way. Furthermore, the finite part is independent of the choice of cutoff
prescription used.