title:
The Schwinger Model on the lattice in the Microcanonical Fermionic
  Average approach

abstract:
  The Microcanonical Fermionic Average method has been used so far in the
context of lattice models with phase transitions at finite coupling. To test
its applicability to Asymptotically Free theories, we have implemented it in
QED$_2$, \it i.e.\rm the Schwinger Model. We exploit the possibility, intrinsic
to this method, of studying the whole $\beta, m$ plane at negligible computer
cost, to follow constant physics trajectories and measure the $m \to 0$ limit
of the chiral condensate. We recover the continuum result within 3 decimal
places.


title: The Mass Ratio Between Neutrinos and Charged Leptons

abstract:
  In the framework of the recently proposed electroweak theory on a Planck
lattice, we are able to solve approximately the lattice Dyson equation for the
fermion self-energy functions and show that the large difference of charged
lepton and neutrino masses is caused by their very different gauge couplings.
The predicted mass ratio ($10^{-5}\sim 10^{-6}$) between neutrinos and charged
lepton is compatible with present experiments.


title:
The universal effective potential for three-dimensional massive scalar
  field theory from the Monte Carlo study of the Ising model

abstract:
  We study the low-energy effective action $S_{eff}[\varphi]$ for the
one-component real scalar field theory in three Euclidean dimensions in the
symmetric phase, concentrating on its static part --- effective potential
$V_{eff}(\varphi)$. It characterizes the approach to the phase transition in
all systems that belong to the 3d Ising universality class. We compute it from
the probability distributions of the average magnetization in the 3d Ising
model in a homogeneous external field, obtained by Monte Carlo. We find that
the $\varphi^6$ term in $V_{eff}$ is important, while the higher terms can be
neglected within our statistical errors. Thus we obtain the approximate
effective action $$ S_{eff} = \int d^3 x \left\{
  {1 \over 2} \partial_\mu \varphi \partial_\mu \varphi +
  {1 \over 2} m^2 \varphi^2 + m g_4 \varphi^4 + g_6 \varphi^6 \right\} , $$
with arbitrary mass $m$ that sets the scale, and dimensionless couplings $g_4 =
0.97 \pm 0.02$ and $g_6 = 2.05 \pm 0.15$. The value of $g_4$ is consistent with
the renormalization group fixed point coupling. This $V_{eff}$, when used
instead of the traditional $a \varphi^2 + b \varphi^4$, turns the
Ginzburg--Landau description of the long-wave properties of the 3d theory near
criticality into quantitatively accurate. It is also relevant to the theory of
cosmological phase transitions.


title: Tadpole-Improved Perturbation Theory for Heavy-Light Lattice Operators

abstract:
  Lattice calculations of matrix elements involving heavy-light quark bilinears
are of interest in calculating a variety of properties of B and D mesons,
including decay constants and mixing parameters. A large source of uncertainty
in the determination of these properties has been uncertainty in the
normalization of the lattice-regularized operators that appear in the matrix
elements. Tadpole-improved perturbation theory, as formulated by Lepage and
Mackenzie, promises to reduce these uncertainties below the ten per cent level
at one-loop. In this paper we study this proposal as it applies to
lattice-regularized heavy-light operators. We consider both the commonly used
zero-distance bilinear and the distance-one point-split operator. A
self-contained section on the application of these results is included. The
calculation reduces the value of $f_B$ obtained from lattice calculations using
the heavy quark effective theory.


title: The Spontaneous Breaking of Chiral Symmetry without Goldstone Bosons

abstract:
  Considering a self-interaction only of mirror fermions in the context of a
lattice-regularized fermion field theory, we show that the system undergoes
spontaneous breaking of chiral symmetry and mirror-fermion masses are
generated. However, it is explicitly shown that there are no Goldstone bosons
appearing together with this spontaneous symmetry breaking phenomenon, since
Lorentz invariance, one of very general prerequisites of the Goldstone theorem,
is violated. The result and its possible application are briefly discussed.


title: Beauty Physics in Lattice Gauge Theory

abstract:
  We summarize the present status of lattice gauge theory computations of the
leptonic decay constants $f_D$ and $f_B$. The various sources of systematic
errors are explained in a manner easily understood by the non--expert. The
results obtained by the different groups are then systematically compared. As a
result, we derive estimates for $f_D$ and $f_B$ in the quenched approximation
through an appropriate combination of the data available from the different
groups. Since we account for a possible lattice spacing dependence, the final
errors are quite large. However, it is now well known how these uncertainties
can be reduced. For the decay constant of heavy--light pseudoscalar mesons with
masses of 1-2~GeV, an interesting comparison of a full QCD result with the
corresponding simulation in the quenched approximation can be done. Effects of
sea quarks of mass $m_s$ are below the statistical accuracy of these
simulations. Related quantities, like $B$--parameters, the spectrum of
beauty--hadrons and the breaking of the QCD string are discussed briefly.


title: Quenched QCD at finite density

abstract:
  Simulations of quenched $QCD$ at relatively small but {\it nonzero} chemical
potential $\mu$ on $32 \times 16^3$ lattices indicate that the nucleon
screening mass decreases linearly as $\mu$ increases predicting a critical
chemical potential of one third the nucleon mass, $m_N/3$, by extrapolation.
The meson spectrum does not change as $\mu$ increases over the same range, from
zero to $m_\pi/2$. Past studies of quenched lattice QCD have suggested that
there is phase transition at $\mu = m_\pi/2$. We provide alternative
explanations for these results, and find a number of technical reasons why
standard lattice simulation techniques suffer from greatly enhanced
fluctuations and finite size effects for $\mu$ ranging from $m_\pi/2$ to
$m_N/3$. We find evidence for such problems in our simulations, and suggest
that they can be surmounted by improved measurement techniques.


title:
Phase Diagram of An SU(2)xSU(2) Scalar-Fermion Model with Massless
  Decoupled Doublers

abstract:
  We present the phase structure of the chiral SU(2)xSU(2) scalar-fermion model
on the lattice using the Zaragoza proposal for chiral fermions. The numerical
result agrees with an analytic study based on the use of weak and strong Yukawa
coupling expansions combined with the mean field approach. The phase diagram
consits of four phases: paramagnetic(PM), ferromagnetic(FM),
antiferromagnetic(AFM) and ferrimagnetic (FI). The transition lines separating
these four phases intersect at one quadruple point.


title: The Well-Defined Phase of Simplicial Quantum Gravity in Four Dimensions

abstract:
  We analyze simplicial quantum gravity in four dimensions using the Regge
approach. The existence of an entropy dominated phase with small negative
curvature is investigated in detail. It turns out that observables of the
system possess finite expectation values although the Einstein-Hilbert action
is unbounded. This well-defined phase is found to be stable for a one-parameter
family of measures. A preliminary study indicates that the influence of the
lattice size on the average curvature is small. We compare our results with
those obtained by dynamical triangulation and find qualitative correspondence.


title: Super-Instantons in Gauge Theories and Troubles with Perturbation Theory

abstract:
  In gauge theories with continuous groups there exist classical solutions
whose energy vanishes in the thermodynamic limit (in any dimension). The
existence of these super-instantons is intimately related to the fact that even
at short distances perturbation theory can fail to produce unique results. This
problem arises only in non-Abelian models and only starting at O(1/beta^2).


title:
A generalized model for two dimensional quantum gravity and dynamics of
  random surfaces for d>1

abstract:
  The possible interpretations of a new continuum model for the two-dimensional
quantum gravity for $d>1$ ($d$=matter central charge), obtained by carefully
treating both diffeomorphism and Weyl symmetries, are discussed. In particular
we note that an effective field theory is achieved in low energy (large area)
expansion, that may represent smooth self-avoiding random surfaces embedded in
a $d$-dimensional flat space-time for arbitrary $d$. Moreover the values of
some critical exponents are computed, that are in agreement with some recent
numerical results.


title:
Chiral Symmetry, Renormalization Group and Fixed Points for Lattice
  Fermions

abstract:
  We discuss fixed point actions for various types of free lattice fermions.
The iterated block spin renormalization group transformation yields lines of
local but chiral symmetry breaking fixed points. For staggered fermions at
least the $U(1) \otimes U(1)$ symmetry can be preserved. This provides a basis
for approximating perfect actions for asymptotically free theories far from the
critical surface. For a class of lattice fermions that includes Wilson fermions
we find in addition one non local but chirally invariant fixed point. Its
vicinity is studied in the framework of the Gross Neveu model with weak four
Fermi interaction.


title:
Spectrum of the Dirac operator in a QCD instanton liquid: two versus
  three colors

abstract:
  Approximating the sum over all gauge field configurations in the QCD
partition function by a liquid of instantons, we calculate the spectrum of the
Dirac operator for two and three colors and for 0, 1 and 2 flavors. We find a
remarkable difference in the spectrum near zero virtuality between 2 and 3
colors, which can be explained in terms of chiral random matrix theory. For two
colors the Dirac operator is real, and the appropriate random matrix ensemble
has real matrix elements. For three colors the Dirac operator is complex, and
the spectrum can be described by a random matrix ensemble with complex matrix
elements. These results provide further evidence that the spectrum near zero
virtuality is universal and is completely determined by symmetries.


title: Loop Action for Lattice U(1) Gauge Theory

abstract:
  It is showed that the very recently introduced Lagrangian $loop$ formulation
of the lattice Maxwell theory is equivalent to the Villain form in 2+1
dimensions. A transparent description of the classical $loop$ action is given
in pure geometrical terms for the $2+1$ and $3+1$ dimensional cases.


title:
Single-Cluster Monte Carlo Study of the Ising Model on Two-Dimensional
  Random Lattices

abstract:
  We use the single-cluster Monte Carlo update algorithm to simulate the Ising
model on two-dimensional Poissonian random lattices with up to 80,000 sites
which are linked together according to the Voronoi/Delaunay prescription. In
one set of simulations we use reweighting techniques and finite-size scaling
analysis to investigate the critical properties of the model in the very
vicinity of the phase transition. In the other set of simulations we study the
approach to criticality in the disordered phase, making use of improved
estimators for measurements. From both sets of simulations we obtain clear
evidence that the critical exponents agree with the exactly known exponents for
regular lattices, i.e., that (lattice) universality holds for the
two-dimensional Ising model.


title: Fractal Dimension of Gauge-fixing Defects

abstract:
  The fractal dimension $D_f$ of sites resisting Landau or maximal Abelian(MA)
gauge fixing in lattice $SU(3)$ gluodynamics is defined and computed. In Landau
gauge such sites clump into $D_f\sim 1$ clusters in the confining phase. In the
finite temperature phase their dimensionality drops to $D_f < 1$, that is,
clustering seems to dissipate. In contrast, MA gauge resistant sites fail to
exhibit a notable tendency to cluster at any temperature.


title: The Chirality of $b$ Quark Couplings

abstract:
  This review addresses the question of the chirality of $b$ quark weak
couplings from a theoretical and from a purely phenomenological point of view.
Due to their small magnitude $b$ decay couplings are subject to possible large
corrections from right-handed terms, on the one hand, and do not affect the
weak interactions of the first two quark families in any observable manner, on
the other hand. This motivated an $SU(2)_L\times SU(2)_R\times U(1)$ model with
purely right-handed $b$-decay couplings. The model is consistent with
experiments, including recent measurements of a lepton forward-backward
asymmetry in $B\to D^*\ell\nu$ and of radiative $B$ decays. Parity violating
asymmetries in semileptonic decays of polarized $\Lambda_b$ baryons produced in
$Z^0$ decays provide a promising way of measuring the chirality of the $b$ to
$c$ current.


title:
Scattering phases on finite lattices in the broken phase of the
  four-dimensional O(4)-\phi^4 theory

abstract:
  According to a proposal of Luescher it is possible to determine elastic
scattering phases in infinite volume from the energy spectrum of two-particle
states in a periodic box. We demonstrate the applicability of this method in
the broken phase of the four-dimensional O(4) non-linear sigma-model in a Monte
Carlo study on finite lattices. This non-perturbative approach also permits the
study of unstable particles, the sigma-particle in our case. We observe the
sigma-resonance and extract its mass and width. In all scattering channels
investigated the results are completely consistent with perturbative
calculations.


title:
Variational description of statistical field theories using Daubechies'
  wavelets

abstract:
  We investigate the description of statistical field theories using
Daubechies' orthonormal compact wavelets on a lattice. A simple variational
approach is used to extend mean field theory and make predictions for the
fluctuation strengths of wavelet coefficients and thus for the correlation
function. The results are compared to Monte Carlo simulations. We find that
wavelets provide a reasonable description of critical phenomena with only a
small number of variational parameters. This lets us hope for an implementation
of the renormalization group in wavelet space.


title: Surface states and chiral symmetry on the lattice

abstract:
  In a Hamiltonian formalism we study chiral symmetry for lattice Fermions
formulated in terms of Shockley surface states bound to a wall in an extra
spatial dimension. For hadronic physics this provides a natural scheme for
taking quark masses to zero without requiring a precise tuning of parameters.
We illustrate the chiral anomaly as a flow of states in this extra dimension.
We discuss two alternatives for extending the picture to a chiral coupling of
gauge fields to such Fermions; one with a small explicit breaking of gauge
symmetry and one one with heavy mirror Fermions.


title:
Strong Coupling Expansion for Scattering Phases in Hamiltonian Lattice
  Field Theories - I. the $(d+1)$-dimensional Ising model

abstract:
  A systematic method to obtain strong coupling expansions for scattering
quantities in Hamiltonian lattice field theories is presented. I develop the
conceptual ideas by means of the Hamiltonian field theory analogue of the Ising
model, in $d$ space and one time dimension. The main result is a convergent
series representation for the sacttering states and the transition matrix. To
be explicit the special cases of $d=1$ and $d=3$ spatial dimensions are
discussed in detail. I compute the next-to-leading order approximation for the
phase shifts. The application of the method to investigate low-energy
scattering phenomena in lattice gauge theory and QCD is proposed.


title:
A Critical Surface of Chiral-invariant System with Gauge Boson and
  Fermions

abstract:
  In the chirally-invariant context of the $U_{em}(1)$ gauge interaction and
four-fermion interactions for ordinary and mirror fermions, the Schwinger-Dyson
equation for the fermion self-energy function is studied on a lattice. We find
that a sensible infrared limit can be defined on a critical surface, which is
consistent with the critical line found in the continuum theory.


title: Looking for the Logarithms in Four-Dimensional Nambu-Jona-Lasinio Models

abstract:
  We study the problem of triviality in the four dimensional Nambu-Jona-Lasinio
model with discrete chiral symmetry using both large-N expansions and lattice
simulations. We find that logarithmic corrections to scaling appear in the
equation of state as predicted by the large-N expansion. The data from $16^4$
lattice simulations is sufficiently accurate to distinguish logarithmically
trivial scaling from power law scaling. Simulations on different lattice sizes
reveal an interesting interplay of finite size effects and triviality. We argue
that such effects are qualitatively different for theories based on fundamental
scalar rather than fermion fields. Several lessons learned here can be applied
to simulations and analyses of more challenging field theories.


title:
Field Theoretic Calculation of the Universal Amplitude Ratio of
  Correlation Lengths in 3D-Ising Systems

abstract:
  In three-dimensional systems of the Ising universality class the ratio of
correlation length amplitudes for the high- and low-temperature phases is a
universal quantity. Its field theoretic determination apart from the
$\epsilon$-expansion represents a gap in the existing literature. In this
article we present a method, which allows to calculate this ratio by
renormalized perturbation theory in the phases with unbroken and broken
symmetry of a one-component $\phi^4$-theory in fixed dimensions $D=3$. The
results can be expressed as power series in the renormalized coupling constant
of either of the two phases, and with the knowledge of their fixed point values
numerical estimates are obtainable. These are given for the case of a two-loop
calculation.


title: Matrix Elements of the Singlet Axial Current in the Proton

abstract:
  We present a method to estimate the matrix element of the singlet axial
current within a polarized proton state using lattice QCD. The method relies on
using the Adler-Bell-Jackiw anomaly and gives the desired result in the chiral
limit. We show that this method fails in the quenched approximation. For heavy
quarks one does not expect much difference between simulations including
dynamical quarks and those done in the quenched approximation. For that reason
we explore numerical methods on an existing set of quenched configurations. The
data obtained in this exploratory study show a poor statistical signal.


title: The spin content of the proton in quenched QCD

abstract:
  We present preliminary results on the proton spin structure function at zero
momentum, in the quenched approximation. Our calculation makes use of a
nonperturbative means of determining the multiplicative renormalization of the
topological charge density.


title:
Algebraic Computation of the Hierarchical Renormalization Group Fixed
  Points and their $\epsilon$-Expansions

abstract:
  Nontrivial fixed points of the hierarchical renormalization group are
computed by numerically solving a system of quadratic equations for the
coupling constants. This approach avoids a fine tuning of relevant parameters.
We study the eigenvalues of the renormalization group transformation,
linearized around the non-trivial fixed points. The numerical results are
compared with $\epsilon$-expansion.


title:
Finite Temperature Phase Transition in SU(2) Lattice Gauge Theory with
  Extended Action

abstract:
  We study the three dimensional fundamental-adjoint $SU(2)$ lattice gauge
theory at finite temperature by Monte Carlo simulations. We find that the
finite temperature deconfinement phase transition line joins the first order
bulk phase transition line at its endpoint. Moreover, across the bulk
transition line, the Polyakov loop undergoes a discontinuous jump implying the
existence of both confining and deconfining phases on its two sides.
Implications for universality and the nature of the confining-deconfining
transition are discussed.


title: Numerical simulation of the Kardar-Parisi-Zhang equation

abstract:
  We simulate the Kardar-Parisi-Zhang equation in 2+1 dimensions. The Hopf-Cole
transformation is used in order to obtain a stable numerical scheme. The two
relevant critical exponents are precisely measured. (2 PostScript figures
available from the authors)


title:
Phase structure of the Higgs-Yukawa systems with chirally invariant
  lattice fermion actions

abstract:
  We develop analytical technique for examining phase structure of $Z_2$,
$U(1)$, and $SU(2)$ lattice Higgs-Yukawa systems with radially frozen Higgs
fields and chirally invariant lattice fermion actions. The method is based on
variational mean field approximation. We analyse phase diagrams of such systems
with different forms of lattice fermion actions and demonstrate that it
crucially depends both on the symmetry group and on the form of the action. We
discuss location in the diagrams of possible non-trivial fixed points relevant
to continuum physics, and argue that the candidates can exist only in $Z_2$
system with SLAC action and $U(1)$ systems with naive and SLAC actions. [Note:
By a product, missing term in Eq. (3.5) of hep-lat/9309010 is reconstructed,
that, however, affects only the result of Sect. 4.3 (Fig. 3) of that reference
(cf. Fig. 2(c) of this paper).]


title: The Nature of the Hadronic String

abstract:
  We study a closed hadronic string using pure glue lattice simulation. We
measure the energy of the flux state encircling the periodic boundary condition
(the torelon). From these data we deduce the string fluctuation component and
compare with models for the hadronic string. [The TEX source file is also
available by anonymous ftp from suna.amtp.liv.ac.uk in directory pub/cmi ]


title: On the equivalence between 2D Yukawa and Gross-Neveu models

abstract:
  We study numerically on the lattice the 2D Yukawa model with the U(1) chiral
symmetry and $N_F$ = 16 at infinite scalar field self-coupling. The scaling
behaviour of the fermion mass, as the Yukawa coupling approaches zero, is
analysed using the mean field method. It is found to agree with that of the
Gross-Neveu model with the same symmetry and $N_F$. The results suggest that
the 2D Yukawa models belong to the universality class of the Gross-Neveu models
not only at weak scalar field self-coupling but also for a broad range of the
bare parameters which is not accessible to the $1/N_F$ expansion. New
universality classes might arise at the crossover to the spin model
universality class, however.


title: Self-avoiding random surfaces with fluctuating topology

abstract:
  A gas of self-avoiding surfaces with an arbitrary polynomial coupling to the
gaussian curvature and an extrinsic curvature term can be realized in a
three-dimensional Ising bcc lattice with only three local couplings. Similar
three parameter realizations are valid also in other lattices. The relation
between the crumpling transition and the roughening is discussed. It turns out
that the mean area of these surfaces is proportional to its genus.


title: External magnetic fields in gauge theories

abstract:
  A general discussion is presented of the response of a gauge-field system to
external magnetic fields, in the light of a theorem due to S. Elitzur. As a
result a natural understanding emerges of some recent puzzling results from
lattice MC simulations, as well as of the phenomenon of ``perfect
diamagnetism'' of non-abelian gauge theories, discovered almost ten years ago.


title: Stochastic Lattice Gas Model for a Predator-Prey System

abstract:
  We propose a stochastic lattice gas model to describe the dynamics of two
animal species population, one being a predator and the other a prey. This
model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was
performed by using a dynamical mean-field approximation and computer
simulations. Our results show that the system exhibits an oscillatory behavior
of the population densities of prey and predators. For the sets of parameters
used in our computer simulations, these oscillations occur at a local level.
Mean-field results predict synchronized collective oscillations.


title: Correlation Function in Ising Models

abstract:
  We simulated the fourier transform of the correlation function of the Ising
model in two and three dimensions using a single cluster algorithm with
improved estimators. The simulations are in agreement with series expansion and
the available exact results in $d=2$, which shows, that the cluster algorithm
can succesfully be applied for correlations. We show as a further result that
our data do not support a hypothesis of Fisher that in any $d=2$ lattice the
fourier transform of the correlation function depends on the lattice generating
function only. In $d=3$ our simulation are again in agreement with the results
from the series expansion, except for the amplitudes $f_{\pm}$, where we find
$f_+/f_-=2.06(1)$.


title: Finite Size Effects in Fluid Interfaces

abstract:
  It is shown that finite size effects in the free energy of a rough interface
of the 3D Ising and three--state Potts models are well described by the
capillary wave model at {\em two--loop} order. The agreement between
theoretical predictions and Monte Carlo simulations strongly supports the idea
of the universality of this description of order--order interfaces in 3D
statistical systems above the roughening temperature.


title: Chirally Extended Quantum Chromodynamics

abstract:
  We propose an extended Quantum Chromodynamics (XQCD) Lagrangian in which the
fermions are coupled to elementary scalar %$\sigma$ and $\pi$ fields through a
Yukawa coupling which preserves chiral invariance. Our principle motivation is
to find a new lattice formulation for QCD which avoids the source of critical
slowing down usually encountered as the bare quark mass is tuned to the chiral
limit. The phase diagram and the weak coupling limit for XQCD are studied. They
suggest a conjecture that the continuum limit of XQCD is the same as the
continuum limit of conventional lattice formulation of QCD. As examples of such
universality, we present the large N solutions of two prototype models for
XQCD, in which the mass of the spurious pion and sigma resonance go to infinity
with the cut-off. Even if the universality conjecture turns out to be false, we
believe that XQCD will still be useful as a low energy effective action for QCD
phenomenology on the lattice. Numerical simulations are recommended to further
investigate the possible benefits of XQCD in extracting QCD predictions.
Postscript files for figures are attached. Search for strings "fig11.ps",
"fig22.ps", "fig33.ps".


title: Towards a Dynamical Solution of the Strong CP Problem

abstract:
  It is argued that QCD might solve the strong CP problem on its own. To test
this idea, a lattice simulation suggests itself. In view of the difficulty of
such a calculation we have, as a first step, investigated the problem in the
$CP^3$ model. The $CP^3$ model is in many respects similar to QCD. In this talk
I shall present some first results of our calculation. Among other things it is
shown that the model has a first order deconfining phase transition in $\theta$
and that the critical value of $\theta$ decreases towards zero as $\beta$ is
taken to infinity. This suggests that $\theta$ is tuned to zero in the
continuum limit.


title: Detecting Dual Superconductivity in the Ground State of Gauge Theory

abstract:
  We explicitly construct a monopole creation operator: its vacuum expectation
value is an order parameter for dual superconductivity, in that, if different
from zero, it signals a spontaneous breaking of the $U(1)$ symmetry
corresponding to monopole charge conservation. This operator is tested by
numerical simulations in compact $U(1)$ gauge theory. Our construction provides
a general recipe for detection of the condensation of any topological soliton.
In particular our operator can be used to detect dual superconductivity of the
QCD vacuum.


title: Nondecoupling of Heavy Mirror-Fermion

abstract:
  According to one-loop perturbation theory, fermions whose masses are totally
generated from Yukawa couplings do not decouple in the heavy mass limit. We
investigate this issue nonperturbatively in the strong coupling regime of the
chiral $U(1)$ mirror-fermion model in four dimensions. Our numerical results,
obtained on $6^3\cdot 16$, $6^3\cdot 24$ and $8^3\cdot 16$ lattices, indicate
nondecoupling of heavy fermion and mirror-fermion, thus supporting the one-loop
picture.


title: Bosonization and the lattice: the $d=2$ Gross-Neveu model

abstract:
  We consider the lattice formulation of bosonized quantum field theories. As a
non trivial example, we study the two dimensional Gross-Neveu model. Analytical
investigations and direct numerical simulation strongly suggest that the
lattice model reproduces the continuum physics. Anticommuting fields are not
required and there are not related doubling problems. (3 PostScript figures
available from the author)


title: Field-strength correlators in $SU(2)$ gauge theory

abstract:
  We measure field-strength and their correlators in presence of a static $q
\bar q$ pair by numerical simulations. We give an interpretation of these data
in terms of quadratic and quartic cumulants.


title: Simplicial Quantum Gravity on a Computer

abstract:
  We describe a method of Monte-Carlo simulations of simplicial quantum gravity
coupled to matter fields. We concentrate mainly on the problem of implementing
effectively the random, dynamical triangulation and building in a
detailed-balance condition into the elementary transformations of the
triangulation. We propose a method of auto-tuning the parameters needed to
balance simulations of the canonical ensemble. This method allows us to prepare
a whole set of jobs and therefore is very useful in systematic determining the
phase diagram in two dimensional coupling space. It is of particular importance
when the jobs are run on a parallel machine.


title: Lattice QCD for Small Computers

abstract:
  These lectures discuss field theoretic techniques that might allow for
realistic simulations of lattice QCD on small computers.


title:
On the Absence of an Exponential Bound in Four Dimensional Simplicial
  Gravity

abstract:
  We have studied a model which has been proposed as a regularisation for four
dimensional quantum gravity. The partition function is constructed by
performing a weighted sum over all triangulations of the four sphere. Using
numerical simulation we find that the number of such triangulations containing
$V$ simplices grows faster than exponentially with $V$. This property ensures
that the model has no thermodynamic limit.


title:
Negative-Energy Spinors and the Fock Space of Lattice Fermions at Finite
  Chemical Potential

abstract:
  Recently it was suggested that the problem of species doubling with
Kogut-Susskind lattice fermions entails, at finite chemical potential, a
confusion of particles with antiparticles. What happens instead is that the
familiar correspondence of positive-energy spinors to particles, and of
negative-energy spinors to antiparticles, ceases to hold for the Kogut-Susskind
time derivative. To show this we highlight the role of the spinorial ``energy''
in the Osterwalder-Schrader reconstruction of the Fock space of non-interacting
lattice fermions at zero temperature and nonzero chemical potential. We
consider Kogut-Susskind fermions and, for comparison, fermions with an
asymmetric one-step time derivative.


title: The Lattice Cutoff for $\lambda\phi^4_4$ and $\lambda\phi^6_3$

abstract:
  We analyze the critical line of $\lambda\phi^4_4$ perturbatively in the bare
coupling $\lambda_0$, by setting the daisy-improved renormalized mass to zero.
By comparing to lattice data, we can then quantify the relation between the
continuum cutoff and the lattice spacing; for the 4-dimensional hypercubic
lattice we find $(\Lambda a)_{C4} = 4.893$. We perform a similar analysis for
$\lambda\phi^6_3$, and find in 3 dimensions $(\Lambda a)_{C3} = 4.67$. We
present two theoretical predictions for $(\Lambda a)$. For small $\lambda_0$,
both the critical line and the renormalized mass near criticality are easily
and accurately calculated from the lattice input parameters.


title:
On the relation between the width of the flux tube and $T_c^{-1}$ in
  lattice gauge theories

abstract:
  Within the framework of a quantum flux tube model for the interquark
potential it is possible to predict that in (2+1) dimensions the space-like
string tension must increase with the temperature in the deconfined phase and
that the thickness of the flux tube must coincide with the inverse of the
deconfinement temperature. Both these predictions are in good agreement with
some recent numerical simulations of SU(2) and $Z_2$ gauge models.


title: Scattering of Glueballs and Mesons in Compact $QED$ in $2+1$ Dimensions

abstract:
  We study glueball and meson scattering in compact $QED_{2+1}$ gauge theory in
a Hamiltonian formulation and on a momentum lattice. We compute ground state
energy and mass, and introduce a compact lattice momentum operator for the
computation of dispersion relations. Using a non-perturbative time-dependent
method we compute scattering cross sections for glueballs and mesons. We
compare our results with strong coupling perturbation theory.


title:
With missing title of the paper. Overrelaxation Algorithm for coupled
  Gauge-Higgs systems

abstract:
  In this letter we extent the overrelaxation algorithm, known to be very
efficient in gauge theories, to coupled gauge-Higgs systems with a particular
emphasis on the update of the radial mode of the Higgs field. Our numerical
tests of the algorithm show that the autocorrelation times can be reduced
substantially.


title: Phase structure and monopoles in U(1) gauge theory

abstract:
  We investigate the phase structure of pure compact U(1) lattice gauge theory
in 4 dimensions with the Wilson action supplemented by a monopole term. To
overcome the suppression of transitions between the phases in the simulations
we make the monopole coupling a dynamical variable. We determine the phase
diagram and find that the strength of the first order transition decreases with
increasing weight of the monopole term, the transition thus ultimately getting
of second order. After outlining the appropriate topological characterization
of networks of currents lines, we present an analysis of the occurring monopole
currents which shows that the phases are related to topological properties.


title: Sphalerons and Other Saddles from Cooling

abstract:
  We describe a new cooling algorithm for SU(2) lattice gauge theory. It has
any critical point of the energy or action functional as a fixed point. In
particular, any number of unstable modes may occur. We also provide insight in
the convergence of the cooling algorithms. A number of solutions will be
discussed, in particular the sphalerons for twisted and periodic boundary
conditions which are important for the low-energy dynamics of gauge theories.
For a unit cubic volume we find a sphaleron energy of resp. $\cE_s=34.148(2)$
and $\cE_s=72.605(2)$ for the twisted and periodic case. Remarkably, the
magnetic field for the periodic sphaleron satisfies at all points $\Tr
B_x^2=\Tr B_y^2=\Tr B_z^2$.


title: The Spatial String Tension in High Temperature Lattice Gauge Theories

abstract:
  We develop some techniques which allow an analytic evaluation of space-like
observables in high temperature lattice gauge theories. We show that such
variables are described extremely well by dimensional reduction. In particular,
by using results obtained in the context of ``Induced QCD'', we evaluate the
contributions to space-like observables coming from the Higgs sector of the
dimensionally reduced action, we find that they are of higher order in the
coupling constant compared to those coming from the space-like action and hence
neglegible near the continuum limit. In the case of SU(2) gauge theory our
results agree with those obtained through Montecarlo simulations both in (2+1)
and (3+1) dimensions and they also indicate a possible way of removing the gap
between the two values of $g^2(T)$ recently appeared in the literature.


title:
Computation of the Heavy-Light Decay Constant using Non-relativistic
  Lattice QCD

abstract:
  We report results on a lattice calculation of the heavy-light meson decay
constant employing the non-relativistic QCD approach for heavy quark and Wilson
action for light quark. Simulations are carried out at $\beta=6.0$ on a
$16^3\times 48$ lattice. Signal to noise ratio for the ground state is
significantly improved compared to simulations in the static approximation,
enabling us to extract the decay constant reliably. We compute the heavy-light
decay constant for several values of heavy quark mass and estimate the
magnitude of the deviation from the heavy mass scaling law $f_{P} \sqrt{m_{P}}
= const$. For the $B$ meson we find $f_{B} = 171\pm 22^{+19}_{-45}$ MeV, while
an extrapolation to the static limit yields $f_{B}^{static}$ = $297\pm
36^{+15}_{-30}$ MeV.


title: Instanton size distribution in O(3)

abstract:
  We present calculations of the size distribution of instantons in the 2d O(3)
non-linear sigma-model, and briefly discuss the effects cooling has upon the
configurations and the topological objects. (This preprint is also available
via anonymous ftp to suna.amtp.liv.ac.uk in /pub/pss/ as instdist.uue.)


title: Critical Point Correlation Function for the 2D Random Bond Ising Model

abstract:
  High accuracy Monte Carlo simulation results for 1024*1024 Ising system with
ferromagnetic impurity bonds are presented. Spin-spin correlation function at a
critical point is found to be numerically very close to that of a pure system.
This is not trivial since a critical temperature for the system with impurities
is almost two times lower than pure Ising $T_c$. Finite corrections to the
correlation function due to combined action of impurities and finite lattice
size are described.


title: Reentrant Behavior in the Domany-Kinzel Cellular Automaton

abstract:
  We present numerical and analytical results for a special kind of
one-dimensional probabilistic cellular automaton, the so called Domany-Kinzel
automaton. It is shown that the phase boundary separating the active and the
recently found chaotic phase exhibits reentrant behavior. Furthermore exact
results for the $p_2$=0-line are discussed.


title: Four-Quark Binding Energies from SU(2) Lattice Monte Carlo

abstract:
  Energies of four-quark systems have been extracted in a static quenched SU(2)
lattice Monte Carlo calculation for six different geometries, both planar and
non-planar, with $\beta=2.4$ and lattice size $16^3\times 32$. In all cases, it
is found that the binding energy is greatly enhanced when the four quarks can
be partitioned in two ways with comparable energies. Also it is shown that the
energies of the four-quark states cannot be understood simply in terms of
two-quark potentials.


title: The Propagators of Gauge Bosons on a lattice

abstract:
  We analyse the problem of the generation of mass in the gauge boson sector on
the (Planck) lattice. We obtain a dynamical scenario quite similar to the
popular Higgs-mechanism, with the important difference that no Higgs-type
excitation is present in our theory. By fixing the mass of the $Z^\circ$-boson
and the renormalized gauge couplings at their experimental values, we get for
the top quark mass $m_t\simeq 149$GeV and for the $\rho$-parameter the very
small value $\rho\sim 10^{-6}$.


title: QCD thermodynamics with Wilson quarks at large kappa

abstract:
  We have extended our study of the high temperature transition with two
flavors of Wilson quarks on 12^3 x 6 lattices to kappa=0.19. We have also
performed spectrum calculations on 12^3 x 24 lattices at kappa=0.19 to find the
physical lattice spacing and quark mass. At this value of kappa the transition
is remarkable in that the plaquette and psi-bar-psi show a large discontinuity
while the Polyakov loop changes very little. This and several other features of
the transition are more suggestive of a bulk transition than a transition to a
quark-gluon plasma. However, if the temperature is estimated using the rho mass
as a standard, the result is about 150 MeV, in agreement with the value found
for the thermal transition with Kogut-Susskind quarks. uuencoded compressed
Postscript file


title: Distances on a Lattice from Non-commutative Geometry

abstract:
  Using the tools of noncommutative geometry we calculate the distances between
the points of a lattice on which the usual discretized Dirac operator has been
defined. We find that these distances do not have the expected behaviour,
revealing that from the metric point of view the lattice does not look at all
as a set of points sitting on the continuum manifold. We thus have an
additional criterion for the choice of the discretization of the Dirac
operator.


title:
Screening and Deconfinement of Sources in Finite Temperature SU(2)
  Lattice Gauge Theory

abstract:
  Deconfinement and screening of higher-representation sources in
finite-temperature $SU(2)$ lattice gauge theory is investigated by both
analytical and numerical means. The effective Polyakov-line action at strong
coupling is simulated by an efficient cluster-updating Monte Carlo algorithm
for the case of $d\!=\!4$ dimensions. The results compare very favourably with
an improved mean-field solution. The limit $d\!\to\!\infty$ of the $SU(2)$
theory is shown to be highly singular as far as critical behaviour is
concerned. In that limit the leading amplitudes of higher representation
Polyakov lines vanish at strong coupling, and subleading exponents become
dominant. Each of the higher-representation sources then effectively carry with
them their own critical exponents.


title: Lattice and Continuum Theories

abstract:
  We investigate path integral formalism for continuum theory. It is shown that
the path integral for the soft modes can be represented in the form of a
lattice theory. Kinetic term of this lattice theory has a standard form and
potential term has additional nonlocal terms which contributions should tend to
zero in the limit of continuum theory. Contributions of these terms can be
estimated. It is noted that this representation of path integral may be useful
to improve lattice calculations taking into account hard modes contribution by
standard perturbative expansion. We discuss translation invariance of
correlators and the possibility to construct a lattice theory which keeps
rotary invariance also.


title:
Lattice Computation of the Effective Potential in O(2)-Invariant
  $\lambda\Phi^4$ Theory

abstract:
  We present a lattice computation of the effective potential for
O(2)-invariant $(\lambda\Phi^4)_4$ theory in the region of bare parameters
corresponding to a classically scale-invariant theory. As expected from
``triviality'' and as in the one-component theory, we find very good agreement
with the one-loop prediction, while a perturbative leading-log improvement of
the effective potential fails to reproduce the Monte Carlo data. The mass $m_h$
of the free shifted radial field is related to the renormalized vacuum
expectation value $v_R$ through the same relation $m^2_h=8\pi^2 v^2_R$ as in
the one-component case. This confirms the prediction of a weakly interacting
2.2 TeV Higgs particle in the standard model.


title: Critical region of the random bond Ising model

abstract:
  We describe results of the cluster algorithm Special Purpose Processor
simulations of the 2D Ising model with impurity bonds. Use of large lattices,
with the number of spins up to $10^6$, permitted to define critical region of
temperatures, where both finite size corrections and corrections to scaling are
small. High accuracy data unambiguously show increase of magnetization and
magnetic susceptibility effective exponents $\beta$ and $\gamma$, caused by
impurities. The $M$ and $\chi$ singularities became more sharp, while the
specific heat singularity is smoothed. The specific heat is found to be in a
good agreement with Dotsenko-Dotsenko theoretical predictions in the whole
critical range of temperatures.


title: A New Determination of M_b Using Lattice QCD

abstract:
  Recent results from lattice QCD simulations provide a realistic picture,
based upon first principles, of~$\Upsilon$ physics. We combine these results
with the experimentally measured mass of the $\Upsilon$~meson to obtain an
accurate and reliable value for the $b$-quark's pole mass. We use two different
methods, each of which yields a mass consistent with $M_b = 5.0(2)$~GeV. This
corresponds to a bare mass of $M_b^0 = 4.0(1)$~GeV in our lattice theory and an
$\msbar$~mass of $M_b^\msbar(M_b)=4.0(1)$~GeV. We discuss the implications of
this result for the $c$-quark mass.
*******************************************************************************
THIS IS THE VERSION WHICH WILL BE PUBLISHED IN PRL. SUBSTANTIAL MATERIAL HAS
BEEN ADDED, INCLUDING RESULTS WITH DYNAMICAL FERMIONS AND A CALCULATION OF THE
MSBAR MASS.
*******************************************************************************


title:
Accelerating Wilson Fermion Matrix Inversions by Means of the Stabilized
  Biconjugate Gradient Algorithm

abstract:
  The stabilized biconjugate gradient algorithm BiCGStab recently presented by
van der Vorst is applied to the inversion of the lattice fermion operator in
the Wilson formulation of lattice Quantum Chromodynamics. Its computational
efficiency is tested in a comparative study against the conjugate gradient and
minimal residual methods. Both for quenched gauge configurations at beta= 6.0
and gauge configurations with dynamical fermions at beta=5.4, we find BiCGStab
to be superior to the other methods. BiCGStab turns out to be particularly
useful in the chiral regime of small quark masses.


title: String Tension from Monopoles in SU(2) Lattice Gauge Theory

abstract:
  The axis for Figure 2 was wrong. It has been fixed and the postscript file
replaced (The file was called comp.ps).


title: Monopoles and string tension in SU(2) QCD

abstract:
  Monopole and photon contributions to abelian Wilson loops are calculated
using Monte-Carlo simulations of SU(2) QCD in the maximally abelian gauge. The
string tension is well reproduced only by monopole contributions, whereas
photons alone are responsible for the Coulomb coefficient of the abelian static
potential.


title: High Precision Renormalization Group Study of the Roughening Transition

abstract:
  We confirm the Kosterlitz-Thouless scenario of the roughening transition for
three different Solid-On-Solid models: the Discrete Gaussian model, the
Absolute-Value-Solid-On-Solid model and the dual transform of the XY model with
standard (cosine) action. The method is based on a matching of the
renormalization group flow of the candidate models with the flow of a bona fide
KT model, the exactly solvable BCSOS model. The Monte Carlo simulations are
performed using efficient cluster algorithms. We obtain high precision
estimates for the critical couplings and other non-universal quantities. For
the XY model with cosine action our critical coupling estimate is
$\beta_R^{XY}=1.1197(5)$. For the roughening coupling of the Discrete Gaussian
and the Absolute-Value-Solid-On-Solid model we find $K_R^{DG}=0.6645(6)$ and
$K_R^{ASOS}=0.8061(3)$, respectively.


title: Dual Meissner Effect and String Tension in SU(2) Lattice Gauge Theory

abstract:
  We study the distribution of the color fields due to a static quark-antiquark
pair in SU(2) lattice gauge theory. We find that the London penetration length
measured after Abelian projection in the Abelian Covariant gauge (Maximal
Abelian gauge) agrees with the one obtained without gauge fixing. Moreover the
penetration length scales according to asymptotic freedom. We put out a simple
relation between the penetration length and the string tension.


title: Fast Krylov Space Methods for Calculation of Quark Propogator

abstract:
  Different recently developed Krylov space methods for solving linear systems
are studied and compared for the solution of the Dirac equation on the lattice.
Stabilized Biconjugate Gradient (BiCGstab2) is shown to be a robust and
efficient solver for the calculation of the Wilson quark propagator in lattice
QCD.


title: How good is the quenched approximation of QCD?

abstract:
  The quenched approximation for QCD is, at present and in the foreseeable
future, unavoidable in lattice calculations with realistic choices of the
lattice spacing, volume and quark masses. In this talk, I review an analytic
study of the effects of quenching based on chiral perturbation theory. Quenched
chiral perturbation theory leads to quantitative insight on the difference
between quenched and unquenched QCD, and reveals clearly some of the diseases
which are expected to plague quenched QCD. Uses jnl.tex and epsf.tex for figure
3. Figures 1 and 2 not included, sorry. Available as hardcopy on request.


title: Hadron Masses from the Valence Approximation to Lattice QCD

abstract:
  We evaluate pseudoscalar, vector, spin 1/2 and spin 3/2 baryon masses
predicted by lattice QCD with Wilson quarks in the valence (quenched)
approximation for a range of different values of lattice spacing, lattice
volume and quark mass. Extrapolating these results to physical quark mass, then
to zero lattice spacing and infinite volume we obtain values for eight mass
ratios. We also determine the zero lattice spacing, infinite volume limit of an
alternate set of five quantities found without extrapolation in quark mass.
Both sets of predictions differ from the corresponding observed values by
amounts consistent with the predicted quantities' statistical uncertainties.


title: Axial symmetries in lattice QCD with Kaplan fermions

abstract:
  This paper develops in detail a lattice definition of QCD based on the chiral
defect fermions recently introduced by Kaplan. The revised version provides
missing technical details in the proof that non-singlet axial symmetries become
exact in the limit of an infinite fifth dimension. Also several minor errors
are corrected.


title: Localization in Lattice Gauge Theory and a New Multigrid Method

abstract:
  We show numerically that the lowest eigenmodes of the 2-dimensional
Laplace-operator with SU(2) gauge couplings are strongly localized. A
connection is drawn to the Anderson-Localization problem. A new Multigrid
algorithm, capable to deal with these modes, shows no critical slowing down for
this problem.


title:
Spatial and Temporal Hadron Correlators below and above the Chiral Phase
  Transition

abstract:
  Hadronic correlation functions at finite temperature in QCD, with four
flavours of dynamical quarks, have been analyzed both above and below the
chiral symmetry restoration temperature. We have used both point and extended
sources for spatial as well as temporal correlators. The effect of periodic
temporal boundary conditions for the valence quarks on the spatial meson
correlators has also been investigated. All our results are consistent with the
existence of individual quarks at high temperatures. A measurement of the
residual interaction between the quarks is presented.


title:
The Block Spin Renormalization Group Approach and Two-Dimensional
  Quantum Gravity

abstract:
  A block spin renormalization group approach is proposed for the dynamical
triangulation formulation of two-dimensional quantum gravity. The idea is to
update link flips on the block lattice in response to link flips on the
original lattice. Just as the connectivity of the original lattice is meant to
be a lattice representation of the metric, the block links are determined in
such a way that the connectivity of the block lattice represents a block
metric. As an illustration, this approach is applied to the Ising model coupled
to two-dimensional quantum gravity. The correct critical coupling is
reproduced, but the critical exponent is obscured by unusually large finite
size effects.


title: The random lattice as a regularization scheme

abstract:
  A semi-analytic method to compute the first coefficients of the
renormalization group functions on a random lattice is introduced. It is used
to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized
on a random lattice has the correct continuum limit. A degree $\kappa$ of
``randomness'' in the lattice is introduced and an estimate of the ratio
$\Lambda_{random}/\Lambda_{regular}$ for two rather opposite values of $\kappa$
in the $\sigma$-model is also given. This ratio turns out to depend on
$\kappa$.


title: Three-Dimensional Integrable Models and Associated Tangle Invariants

abstract:
  In this paper we show that the Boltzmann weights of the three-dimensional
Baxter-Bazhanov model give representations of the braid group, if some suitable
spectral limits are taken. In the trigonometric case we classify all possible
spectral limits which produce braid group representations. Furthermore we prove
that for some of them we get cyclotomic invariants of links and for others we
obtain tangle invariants generalizing the cyclotomic ones.


title: On the exponential bound in four dimensional simplicial gravity

abstract:
  Simplicial quantum gravity has been proposed as a regularization for four
dimensional quantum gravity. The partition function is constructed by
performing a weighted sum over all triangulations of the 4-sphere. The model is
well-defined only if the number of such triangulations consisting of $N$
simplexes is exponentially bounded. Numerical simulations seem so far to favor
such a bound.


title:
Fractal Wilson Loop - Area Law and Gauge Invariance in Next to Leading
  Order

abstract:
  We consider a fractal Wilson loop $<F_{P}>$ and present physical arguments
why this should be a relevant observable in nature. We show for non-compact
SU(2) lattice gauge theory in the next to leading order of strong coupling
expansion that $<F_{P}>$ obeys an area law behavior and is gauge invariant.


title:
Polyakov Loops and Finite-Size Effects of Hadron Masses in Lattice Full
  Q.C.D

abstract:
  The polarization of Polyakov type loops is responsible for the difference
between quenched and unquenched finite size effects on the QCD mass spectrum.
With a numerical simulation, using different sea quarks boundary conditions, we
show that we can align the spatial Polyakov loops in a predefined direction.
Starting from these results, we propose a procedure to partially remove the
Polyakov type contributions in the meson propagators.


title: Volume dependence of the phase boundary in 4D dynamical triangulation

abstract:
  The number of configurations of the dynamical triangulation model of 4D
euclidean quantum gravity appears to grow faster than exponentially with the
volume, with the implication that the system would end up in the crumpled phase
for any fixed $\kappa_2$ (inverse bare Newton constant). However, a scaling
region is not excluded if we allow $\kappa_2$ to go to infinity together with
the volume.


title: The Effect of Dynamical Gauge Field on the Chiral Fermion on a boundary

abstract:
  We study the effect of dynamical gauge field on the Kaplan's chiral fermion
on a boundary in the strong gauge coupling limit in the extra dimension. To all
orders of the hopping parameter expansion, we prove exact parity invariance of
the fermion propagator on the boundary. This means that the chiral property of
the boundary fermion, which seems to survive even in the presence of the gauge
field from a perturbative point of view, is completely destroyed by the
dynamics of the gauge field.


title: Antiferromagnetic Potts Models on the Square Lattice

abstract:
  We study the antiferromagnetic $q$-state Potts model on the square lattice
for $q=3$ and $q=4$, using the Wang-Swendsen-Koteck\'y Monte Carlo algorithm
and a new finite-size-scaling extrapolation method. For $q=3$ we obtain good
control up to correlation length $\xi \sim 5000$; the data are consistent with
$\xi(\beta) = A e^{2\beta} \beta (1 + a_1 e^{-\beta} + \ldots)$ as
$\beta\to\infty$. For $q=4$ the model is disordered even at zero temperature.


title: Monte Carlo Methods for the Self-Avoiding Walk

abstract:
  This article is a pedagogical review of Monte Carlo methods for the
self-avoiding walk, with emphasis on the extraordinarily efficient algorithms
developed over the past decade.


title: Adiabatic Quantum Transport: Quantization and Fluctuations

abstract:
  Quillen's local index theorem is used to study the charge transport
coefficients (adiabatic curvature) associated to the ground state of a
Schr\"odinger operator for a charged (spinless) particle on a closed, multiply
connected surface. The formula splits the adiabatic curvature into an explicit
integral part and a fluctuating part which has a natural interpretation in
terms of quantum chaos.


title: The SU(3) deconfining phase transition with Symanzik action

abstract:
  We report on the determination of the deconfining temperature in SU(3) pure
gauge theory, using the Symanzik tree level improved action, on lattices of
size 3 x 12^3, 4 x 16^3, 5 x 20^3, 6 x24^3. We find that the asymptotic scaling
violation pattern is similar to the one observed using the Wilson action. We
conclude that the irrelevant operators do not affect, in the range of couplings
considered, the lattice beta function. An analysis based on an effective
coupling formulation shows an apparent improvement.


title:
Four Loop Result in $SU(3)$ Lattice Gauge Theory by a Stochastic Method:
  Lattice Correction to the Condensate

abstract:
  We describe a stochastic technique which allows one to compute numerically
the coefficients of the weak coupling perturbative expansion of any observable
in Lattice Gauge Theory. The idea is to insert the exponential representation
of the link variables $U_\mu(x) \to \exp\{A_\mu(x)/\sqrt\beta\}$ into the
Langevin algorithm and the observables and to perform the expansion in
\beta^{-1/2}. The Langevin algorithm is converted into an infinite hierarchy of
maps which can be exactly truncated at any order. We give the result for the
simple plaquette of SU(3) up to fourth loop order (\beta^{-4}) which extends by
one loop the previously known series.


title: Core -- a New Computational Technique for Lattice Systems

abstract:
  The COntractor REnormalization group (CORE) method, a new approach to solving
Hamiltonian lattice systems, is introduced. The method combines contraction and
variational techniques with the real-space renormalization group approach. It
applies to lattice systems of infinite extent and is ideal for studying phase
structure and critical phenomena. The CORE approximation is systematically
improvable and can treat systems with dynamical fermions. The method is tested
using the 1+1-dimensional Ising model.


title:
Numerical Simulations and the Strength of the Electroweak Phase
  Transition

abstract:
  Numerical simulations are performed to study the finite temperature phase
transition in the SU(2) Higgs model on the lattice. The strength of the first
order phase transition is investigated by determining the latent heat and the
interface tension on $L_t=2$ lattices. The values of the Higgs boson mass
presently chosen are below 50 GeV. Our results are in qualitative agreement
with two-loop resummed perturbation theory.


title:
Scaling with a modified Wilson action which suppresses Z_2 artifacts in
  SU(2) lattice gauge theories

abstract:
  A modified Wilson action which suppresses plaquettes which take negative
values is used to study the scaling behavior of the string tension. The use of
the $\b_E$ scheme gives good agreement with asymptotic two loop results.


title: Finite-Size analysis of the 4-d abelian surface gauge model

abstract:
  We present the results of a finite-size analysis of the four dimensional
abelian surface gauge model. This model is defined assigning abelian variables
to the plaquettes of an hypercubical lattice, and is dual to the four
dimensional Ising model. This last model is known to present a second order
phase transition with mean field critical exponents. We have performed Monte
Carlo simulations on several lattice sizes and high statistics. The analysis of
the partition function zeroes and the specific heat scaling behaviour allowed
us to estimate the critical coupling $\beta_c$ as well as the critical
exponents $\nu$ and $\alpha$. Our results are consistent with the second order
critical exponents $\nu = 1/2$ and $\alpha = 0$. The $\beta_c$ value is in
perfect agreement with duality predictions from the 4-d Ising model.
Nevertheless, the energy histograms show a seemingly non-vanishing double peak
structure. The interface tension analysis suggests that this may be a finite
size effect.


title: Exploratory Study of the 3-Gluon Vertex on the Lattice

abstract:
  We define and evaluate on the lattice the amputated 3-gluon vertex function
in momentum space.
  We give numerical results for $16^3 \times 40$ and $24^3 \times 40$ quenched
lattices at $\beta=6.0$.
  A good numerical signal is obtained, at the price of enforcing the
gauge-fixing condition with high accuracy.
  By comparing results from two different lattice volumes, we try to
investigate the crucial issue of finite volume effects.
  We also outline a method for the lattice evaluation of the QCD running
coupling constant as defined from the 3-gluon vertex, while being aware that a
realistic calculation will require larger $\beta$ values and very high
statistics.


title:
Detecting Dual Superconductivity in the Ground State of Gauge Theories -
  II

abstract:
  A monopole creation operator is constructed: its vacuum expectation value is
an order parameter for dual superconductivity in that, if different from zero
it signals spontaneous breaking of the U(1) symmetry corresponding to monopole
charge conservation. The operator is tested on compact U(1) gauge theory on
lattice. For SU(2) gauge theory it clearly demonstrates that confinement is
produced by dual superconductivity.


title:
Simulations of Dynamically Triangulated Gravity -- an Algorithm for
  Arbitrary Dimension

abstract:
  Recent models for discrete euclidean quantum gravity incorporate a sum over
simplicial triangulations. We describe an algorithm for simulating such models
in general dimensions. As illustration we show results from simulations in four
dimensions


title: Gauge-Invariant Noncompact Lattice Simulations

abstract:
  Three techniques for performing gauge-invariant, noncompact lattice
simulations of nonabelian gauge theories are discussed.
  In the first method, the action is not itself gauge invariant, but a kind of
lattice gauge invariance is restored by random compact gauge transformations
during the successive sweeps of the simulation. This method has been applied to
pure $SU(2)$ gauge theory on a $12^4$ lattice, and Wilson loops have been
measured at strong coupling, $\beta=0.5$. These Wilson loops display a
confinement signal not seen in simulations performed earlier with the same
action but without the random gauge transformations.
  In the second method, the action is gauge symmetrized by integrations over
the group manifold.
  The third method is based upon a new, noncompact form of the action that is
exactly invariant under lattice gauge transformations. The action is a natural
discretization of the classical Yang-Mills action.


title:
Radiative Corrections to the Kinetic Couplings in Nonrelativistic
  Lattice QCD

abstract:
  The heavy-quark mass and wave function renormalizations, energy shift, and
radiative corrections to two important couplings, the so-called kinetic
couplings, in nonrelativistic lattice QCD are determined to leading order in
tadpole-improved perturbation theory. The scales at which to evaluate the
running QCD coupling for these quantities, except the wave function
renormalization, are obtained using the Lepage-Mackenzie prescription. When the
bare quark mass is greater than the inverse lattice spacing, the kinetic
coupling corrections are roughly 10\% of the tree-level coupling strengths;
these corrections grow quickly as the bare quark mass becomes small. A need for
computing the two-loop corrections to the energy shift and mass renormalization
is demonstrated.


title:
Fixed boundary conditions and phase transitions in pure gauge compact
  QED

abstract:
  We have simulated the pure gauge compact QED with fixed boundary conditions,
on lattices from $6^4$ to $16^4$. We argue that a lattice with this fixed
boundary imposition corresponds actually to a lattice with spherical topology.
We have found the presence of a phase transition without any trace of
discontinuity. Moreover, the specific heat and the Binder cumulant are
qualitatively consistent with a second order phase transition. The implications
of this observation on the nature of the compact lattice QED are discussed.


title: Monopole Percolation in pure gauge compact QED

abstract:
  The role of monopoles in quenched compact QED has been studied by measuring
the cluster susceptibility and the order parameter $n_{max}/n_{tot}$ previously
introduced by Hands and Wensley in the study of the percolation transition
observed in non-compact QED. A correlation between these parameters and the
energy (action) at the phase transition has been observed. We conclude that the
order parameter $n_{max}/n_{tot}$ is a sensitive probe for studying the phase
transition of pure gauge compact QED.


title:
Nonassociative Algebras and Nonperturbative Field Theory for
  Hierarchical Models

abstract:
  Hierarchical renormalization group (RG) transformations are related to
nonassociative algebras. These algebras serve as a new basic tool for a
rigorous treatment of global RG flows and the search of nontrivial infrared
fixed points. Convergent expansion methods are presented and analyzed in terms
of algebra norms. It is shown that the infrared fixed points are solutions of a
quadratic equation with an infinite number of unknowns. A continuous manifold
of two dimensional periodic nontrivial fixed points is presented in terms of
theta functions. Local Borel summability of the $\epsilon$- expansion for
n-well fixed points is proved by algebraic methods.


title: Nonperturbative Studies of Quantum Gravity

abstract:
  One of several possibilities to construct a quantum theory of gravity is
employing the Feynman path integral. This approach is plagued by some problems:
the integration measure is not uniquely defined, the Einstein-Hilbert action
unbounded, and perturbation theory nonrenormalizable. To make the path integral
tractable one can approximate the continuous geometry of spacetime by a
simplicial complex. The edge lengths of this lattice are considered as the
dynamical degrees of freedom and Regge calculus is applied. In this work,
numerical simulations using the Regge-Einstein action and a "compact" action
show the occurence of a phase transition. The strength of this transition,
separating a well-defined phase with finite expectation values from an
ill-defined phase, is weaker for the compact action, which might be important
for the continuum limit. To analyze the interaction mechanism of this
formulation of quantum gravity, correlation functions between geometrical
quantities like edge lengths, volume elements, and local curvatures have been
computed. Our results for the two-point functions seem to prefer exchange
particles with an effective mass. To ease treatment of quantum gravity a new
approach is proposed consisting in a transformation of the path integral to the
partition function of a spin system. This facilitates analytical and numerical
calculations considerably. First results for the phase structure in two as in
four dimensions are presented and indicate promising similarities to the
original Regge theory.


title: $\pi NN$ and Pseudoscalar Form Factors from Lattice QCD

abstract:
  The $\pi NN$ form factor $g_{\pi NN}(q^2)$ is obtained from a quenched
lattice QCD calculation of the pseudoscalar form factor $g_P(q^2)$ of the
proton with pion pole dominance. We find that $g_{\pi NN}(q^2)$ fitted with the
monopole form agrees well with the Goldberger-Treiman relation and is much
preferred over the dipole form. The monopole mass is determined to be $0.75 \pm
0.14 {\rm GeV}$ which shows that $g_{\pi NN}(q^2)$ is rather soft. The
extrapolated $\pi N$ coupling constant $g_{\pi NN} = 12.7 \pm 2.4$ is quite
consistent with the phenomenological values. We also compare $g_{\pi NN}(q^2)$
with the axial form factor $g_A(q^2)$ to check the pion dominance in the
induced pseudoscalar form factor $h_A(q^2)$ vis \`{a} vis chiral Ward identity.


title: Susceptibilities, the Specific Heat and a Cumulant in Two-Flavour QCD

abstract:
  We study the quark mass dependence of various response functions, which
contribute to chiral susceptibilities and the specific heat in the staggered
fermion formulation of two-flavour QCD. This yields information about the
critical exponents $\alpha$, $\beta$ and $\delta$. In the case of the chiral
susceptibility, obtained as derivative of the chiral order parameter with
respect to the quark mass, we calculate all contributions. This allows to
construct a cumulant of the order parameter, which is a scaling function and
yields a direct determination of the critical exponent $\delta$. All our
results are consistent with a second order phase transition.


title:
Calculation and Interpretation of Hadron Correlation Functions in
  Lattice QCD

abstract:
  Several new developments in the calculation and interpretation of hadron
density-density correlation functions are presented. The asymptotic behavior of
correlation functions is determined from a tree diagram path integral. A method
is developed to use this behavior to correct for leading image contributions on
a finite periodic spatial lattice and to correct for the finite temporal extent
of the lattice. Equal time correlation functions are shown to determine a sum
of the ground state rms radius plus a polarization correction, and it is shown
how to extract the hadron polarizability from unequal time correlation
functions. Image-corrected correlation functions calculated in quenched lattice
QCD are presented and used to determine the size of the pion and nucleon.


title: Monopole action from vacuum configurations in compact QED

abstract:
  It is possible to derive a monopole action from vacuum configurations
obtained in Monte-Carlo simulations extending the method developed by Swendsen.
We apply the method to compact QED both in the Villain and in the Wilson forms.
The action of the natural monopoles in the Villain case is in fairly good
agreement with that derived by the exact dual transformation. Comparing the
monopole actions, we find (1) the DeGrand-Toussaint monopole definition may be
useful for $\beta_V $ larger than about 0.5, (2) the Villain model well
approximates the Wilson one for $\beta$ smaller than $\beta_c$ and (3) in the
Wilson action the monopole condensation occurs in the confinement phase and
$\beta_c$ may be explained by the energy-entropy balance of monopole loops like
in the Villain case.


title:
A Proposal of a Renormalization Group Transformation for Lattice Field
  Theories

abstract:
  We propose a new Real Space Renormalization Group transformation useful for
Monte Carlo calculations in theories with global or local symmetries. From
relaxation arguments we define the block-spin transformation with two tunable
free parameters, adapted to the system's action. Varying them it is possible to
place the fixed point very close to the simulation point. We show how the
method works in a simple model with global symmetry: the three dimensional XY
model.


title: Effective Scalar Field Theory for the Electroweak Phase Transition

abstract:
  We investigate an effective model for the finite temperature restoration
phase transition of the electroweak theory. It is obtained by dimensional
reduction of the $3+1$ dimensional full theory and by subsequent integration
over all static gauge degrees of freedom. The resulting theory corresponds to a
$3$-dimensional $O(4)$ ferromagnet containing cubic and quartic terms of the
field in its potential function. Possible nonperturbative effects of a magnetic
screening mass are parametrically included in the potential. We analyse the
theory using mean field and numerical Monte Carlo (MC) simulation methods. At
the value of the physical Higgs mass, $m_H=37~{\rm GeV}$, considered in the
present investigation, we find a discontinuous symmetry restoring phase
transition. We determine the critical temperature, order parameter jump,
interface tension and latent heat characteristics of the transition. The Monte
Carlo results indicate a somewhat weaker first order phase transition as
compared to the mean field treatment, demonstrating that non-perturbative
fluctuations of the Higgs field are relevant. This effect is especially
important for the interface tension. Any observation of hard first order
transition could result only from non-perturbative effects related to the gauge
degrees of freedom.


title:
Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two
  versus Four Dimensions

abstract:
  We study a multigrid method for nonabelian lattice gauge theory, the time
slice blocking, in two and four dimensions. For SU(2) gauge fields in two
dimensions, critical slowing down is almost completely eliminated by this
method. This result is in accordance with theoretical arguments based on the
analysis of the scale dependence of acceptance rates for nonlocal Metropolis
updates. The generalization of the time slice blocking to SU(2) in four
dimensions is investigated analytically and by numerical simulations. Compared
to two dimensions, the local disorder in the four dimensional gauge field leads
to kinematical problems.


title: Asymptotic scaling from strong coupling

abstract:
  Strong-coupling analysis of two-dimensional chiral models, extended to 15th
order, allows for the identification of a scaling region where known continuum
results are reproduced with great accuracy, and asymptotic scaling predictions
are fulfilled. The properties of the large-$N$ second-order phase transition
are quantitatively investigated.


title: Fermion production despite fermion number conservation

abstract:
  Lattice proposals for a nonperturbative formulation of the Standard Model
easily lead to a global U(1) symmetry corresponding to exactly conserved
fermion number. The absence of an anomaly in the fermion current would then
appear to inhibit anomalous processes, such as electroweak baryogenesis in the
early universe. One way to circumvent this problem is to formulate the theory
such that this U(1) symmetry is explicitly broken. However we argue that in the
framework of spectral flow, fermion creation and annihilation still in fact
occurs, despite the exact fermion number conservation. The crucial observation
is that fermions are excitations relative to the vacuum, at the surface of the
Dirac sea. The exact global U(1) symmetry prohibits a state from changing its
fermion number during time evolution, however nothing prevents the fermionic
ground state from doing so. We illustrate our reasoning with a model in two
dimensions which has axial-vector couplings, first using a sharp momentum
cutoff, then using the lattice regulator with staggered fermions. The
difference in fermion number between the time evolved state and the ground
state is indeed in agreement with the anomaly. A study of the vacuum energy
shows that the perturbative counterterm needed for restoration of gauge
invariance is insufficient in a nonperturbative setting. For reference we also
study a closely related model with vector couplings, the Schwinger model, and
we examine the emergence of the $\theta$-vacuum structure of both theories.


title: Vortex Loops In The 3-d XY Model

abstract:
  We study the properties of vortex loops in the 3-d XY model. We find that the
phase transition in this model is driven by the condensation of short loops
into percolating loops. Paper comes as a uuencoded compressed tar-file,
containing the complete PostScript file. Total file approx. 220 Kb.


title: Precision Upsilon Spectroscopy from Nonrelativistic Lattice QCD

abstract:
  The spectrum of the Upsilon system is investigated using the Nonrelativistic
Lattice QCD approach to heavy quarks and ignoring light quark vacuum
polarization. We find good agreement with experiment for the Upsilon(1S),
Upsilon(2S), Upsilon(3S) and for the center of mass and fine structure of the
chi_b states. The lattice calculations predict b-bbar D-states with center of
mass at (10.20 +/- 0.07 +/- 0.03)GeV. Fitting procedures aimed at extracting
both ground and excited state energies are developed. We calculate a
nonperturbative dispersion mass for the Upsilon(1S) and compare with
tadpole-improved lattice perturbation theory.


title: Failure of the Regge approach in two dimensional quantum gravity

abstract:
  Regge's method for regularizing euclidean quantum gravity is applied to two
dimensional gravity. We use two different strategies to simulate the Regge path
integral at a fixed value of the total area: A standard Metropolis simulation
combined with a histogramming method and a direct simulation using a Hybrid
Monte Carlo algorithm. Using topologies with genus zero and two and a scale
invariant integration measure, we show that the Regge method does not reproduce
the value of the string susceptibility of the continuum model. We show that the
string susceptibility depends strongly on the choice of the measure in the path
integral. We argue that the failure of the Regge approach is due to spurious
contributions of reparametrization degrees of freedom to the path integral.


title: Canonical Demon Monte Carlo Renormalization Group

abstract:
  We describe a new method to compute renormalized coupling constants in a
Monte Carlo renormalization group calculation. The method can be used for a
general class of models, e.g., lattice spin or gauge models. The basic idea is
to simulate a joint system of block spins and canonical demons. In contrast to
the Microcanonical Renormalization Group invented by Creutz et al. our method
does not suffer from systematical errors stemming from a simultaneous use of
two different ensembles. We present numerical results for the $O(3)$ nonlinear
$\sigma$-model.


title: The critical behaviour of Ising spins on 2D Regge lattices

abstract:
  We performed a high statistics simulation of Ising spins coupled to 2D
quantum gravity on toroidal geometries. The tori were triangulated using the
Regge calculus approach and contained up to $512^2$ vertices. We used a
constant area ensemble with an added $R^2$ interaction term, employing the
$dl/l$ measure. We find clear evidence that the critical exponents of the Ising
phase transition are consistent with the static critical exponents and do not
depend on the coupling strength of the $R^2$ interaction term. We definitively
can exclude for this type of model a behaviour as predicted by Boulatov and
Kazakov [Phys. Lett. {\bf B186}, 379 (1987)] for Ising spins coupled to
dynamically triangulated surfaces.


title:
Distribution of the color fields around static quarks: Flux tube
  profiles

abstract:
  We report detailed calculations of the profiles of energy and action
densities in the quark-antiquark string in SU(2) lattice gauge theory.


title: Phase of the Wilson Line

abstract:
  This paper discusses the global $Z(N)$ symmetry of finite-temperature,
$SU(N)$, pure Yang-Mills lattice gauge theory and the physics of the phase of
the Wilson line expectation value. In the high $T$ phase, $\langle L \rangle$
takes one of $N$ distinct values proportional to the $Nth$ roots of unity in
$Z(N)$, and the $Z(N)$ symmetry is broken. Only one of these is consistent with
the usual interpretation $\langle L \rangle = e^{-F/T}$. This relation should
be generalized to $\langle L \rangle = z e^{-F/T}$ with $z \in Z(N)$ so that it
is consistent with the negative or complex values. In the Hamiltonian
description, the {\em physical} variables are the group elements on the links
of the spatial lattice. In a Lagrangian formulation, there are also group
elements on links in the inverse-temperature direction from which the Wilson
line is constructed. These are unphysical, auxiliary variables introduced to
enforce the Gauss law constraints. The following results are obtained: The
relation $\langle L \rangle=ze^{-F/T}$ is derived. The value of $z \in Z(N)$ is
determined by the external field that is needed for the infinite-volume limit.
There is a single physical, high-temperature phase, which is the same for all
$z$. The global $Z(N)$ symmetry is not physical; it acts as the identity on all
physical states. In the Hamiltonian formulation, the high-temperature phase is
not distinguished by physical broken symmetry but rather by percolating flux.


title: Rough Interfaces Beyond the Gaussian Approximation

abstract:
  We compare predictions of the Capillary Wave Model beyond its Gaussian
approximation with Monte Carlo results for the energy gap and the surface
energy of the 3D Ising model in the scaling region. Our study reveals that the
finite size effects of these quantities are well described by the Capillary
Wave Model, expanded to two--loop order ( one order beyond the Gaussian
approximation).


title: Nonuniformity of the $1/N$ Expansion for Two-Dimensional $O(N)$ Models

abstract:
  We point out that the $1/N$ expansion, which is widely invoked to infer
properties of the $2D$ $O(N)$ models, is nonuniform in the temperature, i.e.
with decreasing temperature the $1/N$ expansion truncated at a fixed order
deviates more and more from the true answer. This fact precludes the use of the
expansion to deduce low temperature properties such as asymptotic scaling for
those models. By contrast, in the $1D$ $O(N)$ chains, there are no signs of
such a nonuniformity.


title:
Large Energy Cumulants in the 2D Potts Model and their Effects in Finite
  Size Analysis

abstract:
  We develop an ansatz for expressing the free energy of the two dimensional
$q$-states Potts model for $q > 4$ near its first order phase transition point.
We notice that for the moderate values of $ q \lesssim 15 $, the energy profile
at the phase transition is not expressible as a sum of gaussians. We discuss
how this affects the traditional finite size analysis of this phase transition.
In particular, the dominant length scale governing the finite size corrections
turns out to be much (${} \sim 6$ ~times) larger than the largest correlation
length in the problem.


title: Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group

abstract:
  We study the pure gauge model on a lattice manifold with trivial fundamental
homotopy group, homotopically equivalent to an $S_4$. Monopole loops may
fluctuate freely on that lattice without restrictions due to the boundary
conditions. For the original Wilson action on the hypertorus there is an
established two-state signal in energy distribution functions which disappears
for the new geometry. Our finite size scaling analysis suggests stringent upper
bounds on possible discontinuities in the plaquette action. However, no
consistent asymptotic finite size scaling behaviour is observed.


title:
Multibondic Cluster Algorithm for Monte Carlo Simulations of First-Order
  Phase Transitions

abstract:
  Inspired by the multicanonical approach to simulations of first-order phase
transitions we propose for $q$-state Potts models a combination of cluster
updates with reweighting of the bond configurations in the
Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests
for the two-dimensional models with $q=7, 10$ and $20$ show that the
autocorrelation times of this algorithm grow with the system size $V$ as $\tau
\propto V^\alpha$, where the exponent takes the optimal random walk value of
$\alpha \approx 1$.


title: Investigation of Laplacian Gauge Fixing for U(1) and SU(2) Gauge Fields

abstract:
  The Laplacian gauge on the lattice is investigated numerically using U(1) and
SU(2) gauge fields. The problem of Gribov ambiguities is addressed and to asses
the smoothness of the gauge fixed configurations, they are compared to
configurations fixed to the Landau gauge. The results of these comparisons with
the Landau gauge indicate that Laplacian gauge fixing works very well in
practice and offers a viable alternative to Landau gauge fixing.


title:
Comment on A. Patrascioiu and E. Seiler's paper ``Nonuniformity of the
  $1/N$ Expansion for Two-Dimensional $O(N)$ Models''

abstract:
  We remind that the non-uniformity in the temperature of the $1/N$ expansion
for dimensionful quantities pointed out in Patrascioiu and Seiler's paper is
not only compatible with but is predicted by asymptotic freedom, and it is
present in the continuum as well as on the lattice. The convergence of the
$1/N$ expansion for adimensional quantities is perfectly uniform.


title: Compact Lattice QED with Staggered Fermions and Chiral Symmetry Breaking

abstract:
  Different formulations of the $4d$ compact lattice QED with staggered
fermions (standard Wilson and modified by suppression of lattice artifacts) are
investigated by Monte Carlo simulations within the quenched approximation. We
show that after suppressing lattice artifacts the system undergoes a phase
transition from the Coulomb phase into a presumably weakly chirally broken
phase only at (unphysical) negative $\beta$--values.


title: Simulation of Field Theories in Wavelet Representation

abstract:
  The field is expanded in a wavelet series and the wavelet coefficients are
varied in a simulation of the 2D $\phi^4$ field theory. The drastically reduced
autocorrelations result in a substantial decrease of computing requirements,
compared to those in local Metropolis simulations. A large part of the
improvement is shown to be the result of an additional freedom in the choice of
the allowed range of change at the Metropolis update of wavelet components,
namely the range can be optimized independently for all wavelet sizes.


title:
Scaling in the Positive Plaquette Model and Universality in SU(2)
  Lattice Gauge Theory

abstract:
  We investigate universality, scaling, the beta-function and the topological
charge in the positive plaquette model for SU(2) lattice gauge theory.
Comparing physical quantities, like the critical temperature, the string
tension, glueball masses, and their ratios, we explore the effect of a complete
suppression of a certain lattice artifact, namely the negative plaquettes, for
SU(2) lattice gauge theory. Our result is that this modification does not
change the continuum limit, i.e., the universality class. The positive
plaquette model and the standard Wilson formulation describe the same physical
situation. The approach to the continuum limit given by the beta-function in
terms of the bare lattice coupling, however, is rather different: the
beta-function of the positive plaquette model does not show a dip like the
model with standard Wilson action.


title:
An Exploratory Study of Nucleon-Nucleon Scattering Lengths in Lattice
  QCD

abstract:
  An exploratory study is made of the nucleon-nucleon $s$-wave scattering
lengths in quenched lattice QCD with the Wilson quark action. The $\pi$-$N$ and
$\pi$-$\pi$ scattering lengths are also calculated for comparison. The
calculations are made with heavy quarks corresponding to $m_\pi/m_\rho\approx
0.73-0.95$. The results show that the $N$-$N$ system has an attractive force in
both spin-singlet and triplet channels, with their scattering lengths
significantly larger than those for the $\pi$-$N$ and $\pi$-$\pi$ cases, a
trend which is qualitatively consistent with the experiment. Problems toward a
more realistic calculation for light quarks are discussed.


title:
Probing with Penguins: A lattice calculation of the branching ratio for
  some of the exclusive modes of $b \to s \gamma$

abstract:
  We calculate the leading-order matrix element for exclusive decays of $b \to
s\gamma$ in the quenched approximation of lattice QCD on a $24^3\times48$
lattice at $\beta=6.2$, using an O(a)-improved fermion action. The matrix
element is used to extract the on-shell form factor $T_1(q^2=0)$ for $B \to
K^*\gamma$ and $B_s \to \phi\gamma$, using two different assumptions about the
$q^2$ dependence of the form factors for these decays. For $B \to K^*\gamma$,
$T_1(q^2=0)$ is determined to be $0.159^{+34}_{-33}\pm 0.067$ or
$0.124^{+20}_{-18} \pm 0.022$ in the two cases. We find the results to be
consistent (in the Standard Model) with the CLEO experimental branching ratio
of $BR(B\to K^*\gamma) = (4.5 \pm 1.5 \pm 0.9) \times 10^{-5}$.


title: Curvature and scaling in 4D dynamical triangulation

abstract:
  We study the average number of simplices $N'(r)$ at geodesic distance $r$ in
the dynamical triangulation model of euclidean quantum gravity in four
dimensions. We use $N'(r)$ to explore definitions of curvature and of effective
global dimension. An effective curvature $R_V$ goes from negative values for
low $\kappa_2$ (the inverse bare Newton constant) to slightly positive values
around the transition $\kappa_2^c$. Far above the transition $R_V$ is hard to
compute. This $R_V$ depends on the distance scale involved and we therefore
investigate a similar explicitly $r$ dependent `running' curvature $R_{\rm
eff}(r)$. This increases from values of order $R_V$ at intermediate distances
to very high values at short distances. A global dimension $d$ goes from high
values in the region with low $\kappa_2$ to $d=2$ at high $\kappa_2$. At the
transition $d$ is consistent with 4. We present evidence for scaling of $N'(r)$
and introduce a scaling dimension $d_s$ which turns out to be approximately 4
in both weak and strong coupling regions. We discuss possible implications of
the results, the emergence of classical euclidean spacetime and a possible
`triviality' of the theory.


title:
Manifestation of Sea Quark Effects in the Strong Coupling Constant in
  Lattice QCD

abstract:
  We demonstrate that sea quark effects of a magnitude expected from
renormalization group considerations are clearly visible in the strong coupling
constant measured in current full QCD simulations. Building on this result an
estimate of $\alpha_{\overline{MS}}^{(5)}(M_Z)$ is made employing the
charmonium $1S-1P$ mass splitting calculated on full QCD configurations
generated with two flavors of dynamical Kogut-Susskind quarks to fix the scale.


title: Fractal Structure in Two-Dimensional Quantum Regge Calculus

abstract:
  We study the fractal structure of the surface in two-dimensional quantum
Regge calculus by performing Monte Carlo simulation with up to 200,000
triangles. The result can be compared with the universal scaling function
obtained analytically in the continuum limit of dynamical triangulation, which
provides us with a definite criterion whether Regge calculus serves as a proper
regularization of quantum gravity. When the scale-invariant measure is taken as
the measure of the link-length integration, we observe the correct scaling
behavior in the data for the type of loop attached to a baby universe. The data
seem to converge to the universal scaling function as the number of triangles
is increased. The data for the type of loop attached to the mother universe, on
the other hand, shows no scaling behavior up to the present size.


title: The Phases and Triviality of Scalar Quantum Electrodynamics

abstract:
  The phase diagram and critical behavior of scalar quantum electrodynamics are
investigated using lattice gauge theory techniques. The lattice action fixes
the length of the scalar (``Higgs'') field and treats the gauge field as
non-compact. The phase diagram is two dimensional. No fine tuning or
extrapolations are needed to study the theory's critical behovior. Two lines of
second order phase transitions are discovered and the scaling laws for each are
studied by finite size scaling methods on lattices ranging from $6^4$ through
$24^4$. One line corresponds to monopole percolation and the other to a
transition between a ``Higgs'' and a ``Coulomb'' phase, labelled by divergent
specific heats. The lines of transitions cross in the interior of the phase
diagram and appear to be unrelated. The monopole percolation transition has
critical indices which are compatible with ordinary four dimensional
percolation uneffected by interactions. Finite size scaling and histogram
methods reveal that the specific heats on the ``Higgs-Coulomb'' transition line
are well-fit by the hypothesis that scalar quantum electrodynamics is
logarithmically trivial. The logarithms are measured in both finite size
scaling of the specific heat peaks as a function of volume as well as in the
coupling constant dependence of the specific heats measured on fixed but large
lattices. The theory is seen to be qualitatively similar to $\lambda\phi^{4}$.
The standard CRAY random number generator RANF proved to be inadequate


title: Random Geometries and Real Space Renormalization Group

abstract:
  A method of ``blocking'' triangulations that rests on the self-similarity
feature of dynamically triangulated random manifolds is proposed. The method is
used to define the renormalization group for random geometries. As an
illustration, the idea is applied to pure euclidean quantum gravity in two
dimensions. Generalisation to more complicated systems and to higher
dimensionalities of space-time appears straightforward.


title: Deconfinement Transition in Large N Lattice Gauge Theory

abstract:
  We study analytically the phase diagram of the pure $SU(N)$ lattice gauge
theory at finite temperature, and we attempt to estimate the critical
deconfinement temperature. We apply large $N$ techniques to the Wilson and to
the Heat Kernel action, and we study the resulting models both in the strong
coupling and in the weak coupling limits. Using the Heat Kernel action, we
establish an interesting connection between the Douglas-Kazakov phase
transition of two-dimensional QCD and the deconfining transition in $d$
dimensions. The analytic results obtained for the critical temperature compare
well with Montecarlo simulations of the full theory in $(2+1)$ and in $(3+1)$
dimensions.


title: Regge gravity on general triangulations

abstract:
  We investigate quantum gravity in four dimensions using the Regge approach on
triangulations of the four-torus with general, non-regular incidence matrices.
We find that the simplicial lattice tends to develop spikes for vertices with
low coordination numbers even for vanishing gravitational coupling. Different
to the regular, hypercubic lattices almost exclusively used in previous
studies, we find now that the observables depend on the measure. Computations
with nonvanishing gravitational coupling still reveal the existence of a region
with well-defined expectation values. However, the phase structure depends on
the triangulation. Even with additional higher- order terms in the action the
critical behavior of the system changes with varying (local) coordination
numbers.


title: Can Sigma Models Describe Finite Temperature Chiral Transitions?

abstract:
  Large-N expansions and computer simulations indicate that the universality
class of the finite temperature chiral symmetry restoration transition in the
3D Gross-Neveu model is mean field theory. This is a counterexample to the
standard 'sigma model' scenario which predicts the 2D Ising model universality
class. We trace the breakdown of the standard scenario (dimensional reduction
and universality) to the absence of canonical scalar fields in the model. We
point out that our results could be generic for theories with dynamical
symmetry breaking, such as Quantum Chromodynamics.


title: String tension and monopoles in $T \neq 0$ SU(2) QCD

abstract:
  Monopole and photon contributions to abelian Wilson loops are calculated
using Monte-Carlo simulations of finite-temperature $SU(2)$ QCD in the
maximally abelian gauge. Long monopole loops alone are responsible for the
behavior of the string tension in the confinement phase up to the critical
$\beta_c$. Short monopole loops and photons do not contribute to the string
tension. The abelian and the monopole spacial string tensions (both of which
agree with the normal ones for $\beta < \beta_c$) show a $g^{4}(T) T^2$ scaling
behavior in the deconfinement phase. The abelian spacial string tension is in
agreement with the full one even in the deconfinement phase.


title: Low-Temperature Series for the Correlation Length in $d=3$ Ising Model

abstract:
  We extend low-temperature series for the second moment of the correlation
function in $d=3$ simple-cubic Ising model from $u^{15}$ to $u^{26}$ using
finite-lattice method, and combining with the series for the susceptibility we
obtain the low-temperature series for the second-moment correlation length to
$u^{23}$. An analysis of the obtained series by inhomogeneous differential
approximants gives critical exponents $ 2\nu^{\prime} + \gamma^{\prime} \approx
2.55 $ and $ 2\nu^{\prime} \approx 1.27 $.


title: Ising Spins on Thin Graphs

abstract:
  The Ising model on ``thin'' graphs (standard Feynman diagrams) displays
several interesting properties. For ferromagnetic couplings there is a mean
field phase transition at the corresponding Bethe lattice transition point. For
antiferromagnetic couplings the replica trick gives some evidence for a spin
glass phase. In this paper we investigate both the ferromagnetic and
antiferromagnetic models with the aid of simulations. We confirm the Bethe
lattice values of the critical points for the ferromagnetic model on $\phi^3$
and $\phi^4$ graphs and examine the putative spin glass phase in the
antiferromagnetic model by looking at the overlap between replicas in a
quenched ensemble of graphs. We also compare the Ising results with those for
higher state Potts models and Ising models on ``fat'' graphs, such as those
used in 2D gravity simulations.