title: Large $N$ analysis of the Higgs mass triviality bound

abstract:
  We calculate the triviality bound on the Higgs mass in scalar field theory
models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial}
\approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity.
Limits on observable cutoff effects at four percent in several regularized
models with tunable couplings in the bare action yield triviality bounds
displaying a large degree of universality. Extrapolating from $N=\infty$ to
$N=4$ we conservatively estimate that a Higgs particle with mass up to
$0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff
effects, indicating that strong scalar self interactions in the standard model
are not ruled out.
  Note: The full ps file of this preprint is also available via anonymous ftp
to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for
username "anonymous" and for password your name. The file is in the directory
pub/vranas (to go to that directory type: cd pub/vranas) and is called
lrg_n_hig.ps (to get it type: get lrg_n_hig.ps)


title: QCD thermodynamics with two flavors of Wilson quarks at N_t=6

abstract:
  We report on a study of hadron thermodynamics with two flavors of Wilson
quarks on 12^3x6 lattices. We have studied the crossover between the high and
low temperature regimes for three values of the hopping parameter, kappa=0.16,
0.17, and 0.18. At each of these values of kappa we have carried out spectrum
calculations on 12^3x24 lattices for two values of the gauge coupling in the
vicinity of the crossover in order to set an energy scale for our
thermodynamics calculations and to determine the critical value of the gauge
coupling for which the pion and quark masses vanish. For kappa=0.17 and 0.18 we
find coexistence between the high and low temperature regimes over 1,000
simulation time units indicating either that the equilibration time is
extremely long or that there is a possibility of a first order phase
transition. The pion mass is large at the crossover values of the gauge
coupling, but the crossover curve has moved closer to the critical curve along
which the pion and quark masses vanish, than it was on lattices with four time
slices. In addition, values of the dimensionless quantity T_c/m_rho are in
closer agreement with those for staggered quarks than was the case at N_t=4. (A
POSTSCRIPT VERSION OF THIS PAPER IS AVAILABLE BY ANONYMOUS FTP FROM
sarek.physics.ucsb.edu (128.111.8.250) IN THE FILE pub/wilson_thermo.ps)


title:
A Multicanonical Algorithm and the Surface Free Energy in SU(3) Pure
  Gauge Theory

abstract:
  We present a multicanonical algorithm for the SU(3) pure gauge theory at the
deconfinement phase transition. We measure the tunneling times for lattices of
size L^3x2 for L=8,10, and 12. In contrast to the canonical algorithm the
tunneling time increases only moderately with L. Finally, we determine the
interfacial free energy applying the multicanonical algorithm.


title: A new approach to noncompact lattice qed with light fermions

abstract:
  We discuss detailed simulations of the non compact abelian model coupled to
light fermions, using a method previously developed that includes the effects
of the fermionic interactions in an effective action. The approximations
involved are related to an expansion in the flavour number. We address the
problem of the (non) triviality of the theory through a study of the analytical
properties of the effective action as a function of the pure gauge energy. New
numerical results for the plaquette energy, chiral condensate and a qualitative
analysis of the phase diagram are also presented.


title:
Monte Carlo Calculation of Phase Shift in Four Dimensional O(4) $\phi^4$
  Theory

abstract:
  The phase shift of the O(4) symmetric $\phi^4$ theory in the symmetric phase
is calculated numerically using the relation between phase shift and energy
levels of two-particle states recently derived by L\"{u}scher. The results
agree with the prediction of perturbation theory. A practical difficulty of the
method for a reliable extraction of the phase shift for large momenta due to
the necessity of a precise determination of excited two-particle energy levels
is pointed out.


title: Topology of the Yang-Mills Configuration space

abstract:
  It will be described how to uniquely fix the gauge using Coulomb gauge
fixing, avoiding the problem of Gribov copies. The fundamental modular domain,
which represents a one-to-one representation of the set of gauge invariant
degrees of freedom, is a bounded convex subset of the trans- verse gauge
fields. Boundary identifications are the only remnants of the Gribov copies,
and carry all the information about the topology of the Yang-Mills
configuration space. Conversely, the known topology can be shown to imply that
(on a set of measure zero on the boundary) some points of the boundary coincide
with the Gribov horizon. For the low-lying energies, wavefunctionals can be
shown to spread out "across" certain parts of these boundaries. This is how the
topology of Yang-Mills configuration space has an essential influence on the
low-lying spectrum, in a situation where these non- perturbative effects are
not exponentially suppressed.
  This write-up is a short summary, with adequate references, where details on
most of the material I have presented can be found. However, not published
before, is a new observation concerning Henyey's gauge copies.


title: Global Demons in Field Theory : Critical Slowing Down in the Xy Model

abstract:
  We investigate the use of global demons, a `canonical dynamics', as an
approach to simulating lattice regularized field theories. This
deterministically chaotic dynamics is non-local and non-Hamiltonian, and
preserves the canonical measure rather than $\delta(H-E)$. We apply this
inexact dynamics to the 2D XY model, comparing to various implementations of
hybrid Monte Carlo, focusing on critical exponents and critical slowing down.
In addition, we discuss a scheme for making energy non-conserving dynamical
algorithms exact without the use of a Metropolis hit.


title:
Finite Size Scaling of Probability Distributions in SU(2) Lattice Gauge
  Theory and Phi^4 Field Theory

abstract:
  For a system near a second order phase transition, the probability
distribution for the order parameter can be given a finite size scaling form.
This fact is used to compare the finite temperature phase transition for the
Wilson lines in d=3+1 SU(2) lattice gauge theory with the phase transition in
d=3 phi^4 field theory. I exhibit the finite size scaled probability
distributions in the form of a function of two variables (the reduced
`temperature' and the magnetization) for both models. The two surfaces look
identical, and an analysis of the errors also suggests that they are the same.
This strengthens the idea that the SU(2) effective line theory is in the Ising
universality class. I argue for the wider application of the method used here.


title:
Topological susceptibility and string tension in the lattice CP(N)
  models

abstract:
  In the lattice CP(N) models we studied the problems related to the measure of
the topological susceptibility and the string tension . We perfomed numerical
simulations at N=4 and N=10. In order to test the universality, we adopted two
different lattice formulations. Scaling and universality tests led to the
conclusion that at N=10 the geometrical approach gives a good definition of
lattice topological susceptibility. On the other hand, N=4 proved not to be
large enough to suppress the unphysical configurations, called dislocations,
contributing to the topological susceptibility. We obtained other
determinations of the topological susceptibility by the field theoretical
method, wich relies on a local definition of the lattice topological charge
density, and the cooling method. They gave quite consistent results, showing
scaling and universality. The large-N expansion predicts an exponential area
law behavior for sufficiently large Wilson loops, which implies confinement,
due to the dynamical matter fields and absence of the screening phenomenon. We
determined the string tension, without finding evidence of screening effects.


title:
A Lower Bound on $T_{SR}/{m_{\rm H}}$ in the O(4) Model on Anisotropic
  Lattices

abstract:
  Results of an investigation of the $O(4)$ spin model at finite temperature
using anisotropic lattices are presented. In both the large $N$ approximation
and numerical simulations using the Wolff cluster algorithm we find that the
ratio of the symmetry restoration temperature $T_{\rm SR}$ to the Higgs mass
$m_{\rm H}$ is independent of the anisotropy $\xi$. From the numerical
simulations we obtain a lower bound of $T_{\rm SR} / m_{\rm H} \simeq 0.58 \pm
0.02$ at a value for the Higgs mass $m_{\rm H}a_s \simeq 0.5$, which is lowered
further by about $10\%$ at $m_{\rm H}a_s \simeq 1$. Requiring certain timelike
correlation functions to coincide with their spacelike counterparts, quantum
and scaling corrections to the anisotropy are determined and are found to be
small, i.e., the anisotropy is found to be close to the ratio of spacelike and
timelike lattice spacings.


title: Chiral Yukawa models in the planar limit

abstract:
  We consider the most general renormalizable chiral Yukawa model with
$SU(3)_{\rm color}$ replaced by $SU(N_c)$, $SU(2)_{\rm L}$ replaced by $SU(N_w
)$ and $U(1)_{Y}$ replaced by $U(1)^{N_w -1}$ in the limit $N_c
\rightarrow\infty$, $N_w \rightarrow\infty$ with the ratio
$\rho=\sqrt{{N_w}\over{N_c}} \ne 0,\infty$ held fixed. Since for $N_w \ge 3$
only one renormalizable Yukawa coupling per family exists and there is no
mixing between families the limit is appropriate for the description of the
effects of a heavy top quark when all the other fermions are taken to be
massless. A rough estimate of the triviality bound on the Yukawa coupling is
equivalent to $m_t \le 1~TeV$.


title: The Phase Diagram of the $N=2$ Kazakov-Migdal Model

abstract:
  We have determined the phase diagram of the simplest version of a lattice
model introduced in the recent work of Kazakov and Migdal. If $m_0$ and
$\lambda$ are the bare mass and self coupling of the scalar field in the model
respectively, we find a line of first order phase transitions in the ($m_0,
\lambda$) plane ending in a critical point where $\lambda$ is nonzero. Kazakov
and Migdal speculate that their model of scalar field theory could induce QCD.
Our work indicates that for $N=2$ there is no continuum limit for the
Kazakov-Migdal model except at the critical end point. Whether or not a
nontrivial continuum limit exists in the vicinity of the critical point
requires careful study of the renormalization group properties of the model.


title:
Non-Exponential Relaxation Time Scales in Disordered Systems: an
  Application to Protein Dynamics

abstract:
  We study the dynamics of an heteropolymeric chain relaxing toward a new
equilibrium configuration after the action of an external perturbation. We
compare the results from Monte Carlo simulations with the results of a Langevin
normal mode decomposition. We discuss, for sake of comparison, the case of an
ordered homopolymeric chain.


title: Chern-Simons term in the 4-dimensional SU(2) Higgs model

abstract:
  Using a variation of Lueschers geometric charge definition for SU(2) lattice
gauge theory, we have managed to give a geometric expression for it's
Chern-Simons ter. From this definition we have checked the periodic structure.
we determined the Chern-Simons density for symmetric and asymmetric lattices
near the critical region in the SU(2) Higgs model. The data indicate that
tunneling is increased at high temperature.


title: A Parallel Cluster Labeling Method for Monte Carlo Dynamics

abstract:
  We present an algorithm for cluster dynamics to efficiently simulate large
systems on MIMD parallel computers with large numbers of processors. The method
divides physical space into rectangular cells which are assigned to processors
and combines a serial local procedure with a nearest neighbor relaxation
process. By controlling overhead and reducing inter-processor communication
this method attains good performance and speed-up. The complexity and scaling
properties of the algorithm are analyzed.
  The algorithm has been used to simulate large 2d Ising systems (up to 27808 X
27808 sites) with Swendsen-Wang dynamics. Typical updating times on the order
of 82 nanosecs/site and efficiencies larger than 90% have been obtained using
256 processors on the CM-5 supercomputer.


title: A Rigourous Treatment of the Lattice Renormalization Problem of F_B

abstract:
  The $B$-meson decay constant can be measured on the lattice using a $1/m_b$
expansion. To relate the physical quantity to Monte Carlo data one has to know
the renormalization coefficient, $Z$, between the lattice operators and their
continuum counterparts. We come back to this computation to resolve
discrepancies found in previous calculations. We define and discuss in detail
the renormalization procedure that allows the (perturbative) computation of
$Z$. Comparing the one-loop calculations in the effective Lagrangian approach
with the direct two-loop calculation of the two-point $B$-meson correlator in
the limit of large $b$-quark mass, we prove that the two schemes give
consistent results to order $\alpha_s$. We show that there is, however, a
renormalization prescription ambiguity that can have sizeable numerical
consequences. This ambiguity can be resolved in the framework of an $O(a)$
improved calculation, and we describe the correct prescription in that case.
Finally we give the numerical values of $Z$ that correspond to the different
types of lattice approximations discussed in the paper.


title:
Comparison of Lattice Coulomb Gauge Wave Functions in Quenched
  Approximation and with Dynamical Fermions

abstract:
  We present a comparison of Coulomb gauge wave functions from $6/{g^2}=6.0$
quenched simulations with two simulations which include the effects of
dynamical fermions: simulations with two flavors of dynamical staggered quarks
and valence Wilson quarks at $6/{g^2}=5.6$ and simulations with two flavors of
dynamical Wilson quarks and Wilson valence quarks, at $6/{g^2}=5.3$. The
spectroscopy of these systems is essentially identical. Parameterizations of
the wave functions are presented which can be used as interpolating fields for
spectroscopy calculations. The sizes of particles are calculated using these
parameterized wave functions. The resulting sizes are small, approximately half
the sizes of the physical states. The charge radius of the neutron, which
provides an indication of the asymmetries between the wave functions of up and
down quarks, is calculated. Although the size of the nucleon in these
simulations is small, the ratio of the charge radius of the neutron to that of
the proton is consistent with the physical value. We find no significant
differences between the quenched and dynamical simulations.


title: Continuum Gauge Fields from Lattice Gauge Fields

abstract:
  On the lattice some of the salient features of pure gauge theories and of
gauge theories with fermions in complex representations of the gauge group seem
to be lost. These features can be recovered by considering part of the theory
in the continuum. The prerequisite for that is the construction of continuum
gauge fields from lattice gauge fields. Such a construction, which is gauge
covariant and complies with geometrical constructions of the topological charge
on the lattice, is given in this paper. The procedure is explicitly carried out
in the $U(1)$ theory in two dimensions, where it leads to simple results.


title: Introduction to Lattice Gaugefixing and Effective Quark and Gluon Masses

abstract:
  This talk was presented to a non-lattice audience at the June, 1992 Paris
Workshop on QCD Vacuum Structure. We report on the status of quark and gluon
propagators in quenched, gaugefixed lattice QCD. In Landau gauge we find that
the effective quark mass in the chiral limit is $M_q \sim 350(40)MeV$. Quark
and gluon propagators, the slope of the quark dispersion relation, and
effective masses all appear to depend on gauge. A link-chain picture of lattice
gaugefixing in the color $N\to\infty$ and strong coupling limit, where the
system becomes almost solvable, supports the gauge variance of these numerical
results. Subscribers will be given one Postscript file, the Figure included.
Latex and Axis versions available from KY at kyee@rouge.phys.lsu.edu on
request.


title: Phase Transitions in Induced QCD

abstract:
  The variety of the phase transitions in Induced QCD are studied. Depending
upon the parameters in the scalar field potential, there could be infinite
number of fixed points, with different critical behavior. The integral equation
for the density of the eigenvalues of the scalar field are generalized to the
weak coupling phases, with the gap at the origin. We find a wide class of the
massive solutions of these integral equations in the strong coupling phases,
and derive an explicit eigenvalue equation for the scalar branch of the mass
spectrum.


title:
A New Technique for Measuring the Strangemess Content of the Proton on
  the Lattice

abstract:
  A new technique for computing the strangeness content of the proton on the
lattice is described. It is applied to the calculation of the strange quark
contribution to the proton's spin, specifically to the evaluation of the proton
matrix element of the strange quark axial current. Preliminary results are not
in disagreement with the EMC experiment. NOTE: This paper is available only in
postscript form.


title: Gribov Copies and Smeared Correlation Functions in Lattice QCD

abstract:
  We study the influence of Gribov copies in the Coulomb gauge on the smeared
hadronic correlation functions that are involved in the determination of the B
meson decay constant. We find that the residual gauge freedom associated to
Gribov copies induces observable noise effects, though at the level of
numerical accuracy of our simulation these effects are not relevant to the
final determination of f_B. Our results indicate that such effects may become
important on bigger lattices.


title: An Improved Acceptance Procedure for the Hybrid Monte Carlo Algorithm

abstract:
  The probability of accepting a candidate move in the hybrid Monte Carlo
algorithm can be increased by considering a transition to be between windows of
several states at the beginning and end of the trajectory, with a state within
the selected window being chosen according to the Boltzmann probabilities. The
detailed balance condition used to justify the algorithm still holds with this
procedure, provided the start state is randomly positioned within its window.
The new procedure is shown empirically to significantly improve performance for
a test system of uncoupled oscillators.


title: Scaling and Asymptotic Scaling in the SU(2) Gauge Theory

abstract:
  We determine the critical couplings for the deconfinement phase transition in
$SU(2)$ gauge theory on $N_\tau \times N_\sigma^3$ lattices with $N_\tau = 8$
and 16 and $N_\sigma$ varying between 16 and 48. A comparison with string
tension data shows scaling of the ratio $T_c / \sqrt{\sigma}$ in the entire
coupling regime $\beta =2.30-2.75$, while the individual quantities still
exhibit large scaling violations. We find $T_c / \sqrt{\sigma}=0.69(2)$. We
also discuss in detail the extrapolation of $T_c / Lambda_{\rm{\bar{M}
\bar{S}}}$ and $\sqrt{\sigma} / Lambda_{\rm{\bar{M}\bar{S}}}$ to the continuum
limit. Our result, which is consistent with the above ratio, is $T_c /
Lambda_{\rm{\bar{M}\bar{S}}} = 1.23(11)$ and $\sqrt{\sigma} /
Lambda_{\rm{\bar{M}\bar{S}}} = 1.79(12)$. We also comment upon corresponding
results for $SU(3)$ gauge theory and four flavour QCD.


title: Gauge invariant extremization on the lattice

abstract:
  Recently, a method was proposed and tested to find saddle points of the
action in simulations of non-abelian lattice gauge theory. The idea, called
`extremization', is to minimize $\int(\dl S/\dl A_\mu)^2$. The method was
implemented in an explicitly gauge variant way, however, and gauge dependence
showed up in the results.
  Here we show how extremization can be formulated in a way that preserves
gauge invariance on the lattice. The method applies to any gauge group and any
lattice action. The procedure is worked out in detail for the standard
plaquette action with gauge groups U(1) and SU(N).


title:
Noncomputability Arising In Dynamical Triangulation Model Of
  Four-Dimensional Quantum Gravity

abstract:
  Computations in Dynamical Triangulation Models of Four-Dimensional Quantum
Gravity involve weighted averaging over sets of all distinct triangulations of
compact four-dimensional manifolds. In order to be able to perform such
computations one needs an algorithm which for any given $N$ and a given compact
four-dimensional manifold $M$ constructs all possible triangulations of $M$
with $\leq N$ simplices. Our first result is that such algorithm does not
exist. Then we discuss recursion-theoretic limitations of any algorithm
designed to perform approximate calculations of sums over all possible
triangulations of a compact four-dimensional manifold.


title: Duality in Long-Range Ising Ferromagnets

abstract:
  It is proved that for a system of spins $\sigma _i = \pm 1$ having an
interaction energy $-\sum K_{ij} \sigma _i \sigma _j $ with all the $K_{ij}$
strictly positive,one can construct a dual formulation by associating a dual
spin $S_{ijk} = \pm 1$ to each triplet of distinct sites $i,j$ and $k$. The
dual interaction energy reads $-\sum _{(ij)} D_{ij} \prod _{k \neq i,j}
S_{ijk}$ with $tanh(K_{ij})\ = \ exp(-2D_{ij})$, and it is invariant under
local symmetries. We discuss the gauge-fixing procedure, identities relating
averages of order and disorder variables and representations of various
quantities as integrals over Grassmann variables. The relevance of these
results for Polyakov's approach of the 3D Ising model is briefly discussed.


title: Embedding Z(3) in SU(3)

abstract:
  We consider the design of a non-local MonteCarlo algorithm for $SU(3)$
lattice systems according to the idea of {\em embedding} the degrees of freedom
corresponding to the center of the group $Z(3)$. As a crucial ingredient to
reach this goal, we present a practical implementation of a cluster algorithm
for $Z(3)$ systems with general random pair interaction.


title: The triviality bound on the Higgs mass; its value and what it means

abstract:
  Older lattice work exploring the Higgs mass triviality bound is briefly
reviewed. It indicates that a strongly interacting scalar sector in the minimal
standard model cannot exist; on the other hand low energy QCD phenomenology
might be interpreted as an indication that it could. We attack this puzzle
using the $1/N$ expansion and discover a simple criterion for selecting a
lattice action that is more likely to produce a heavy Higgs particle. Depending
on the precise form of the limitation put on the cutoff effects, our large $N$
calculations, when combined with old numerical data, suggest that the Higgs
mass bound might be around 750 $GeV$, which is higher than the $\sim 650~GeV$
previously obtained. Preliminary numerical work indicates that an increase of
at least 19\% takes place at $N=4$ on the $F_4$ lattice when the old simple
action is replaced with a new action (still containing only nearest neighbor
interactions) if one uses the lattice spacing as the physical cutoff for both
actions. It appears that, while a QCD like theory could produce $M_H / F ~ \sim
6$, a meaningful ``minimal elementary Higgs'' theory cannot have $M_H/ F~
\gtapprox 3$. Still, even at 750 $GeV$, the Higgs particle is so wide ($\sim
290~$GeV), that one cannot argue any more that the scalar sector is weakly
coupled.


title:
The Hyperfine Splitting in Charmonium: Lattice Computations Using the
  Wilson and Clover Fermion Actions

abstract:
  We compute the hyperfine splitting $m_{J/\psi}-m_{\eta_c}$ on the lattice,
using both the Wilson and $O(a)$-improved (clover) actions for quenched quarks.
The computations are performed on a $24^3\times48$ lattice at $\beta = 6.2$,
using the same set of 18 gluon configurations for both fermion actions. We find
that the splitting is 1.83\err{13}{15} times larger with the clover action than
with the Wilson action, demonstrating the sensitivity of the spin-splitting to
the magnetic moment term which is present in the clover action. However, even
with the clover action the result is less than half of the physical
mass-splitting. We also compute the decay constants $f_{\eta_c}$ and
$f^{-1}_{J/\psi}$, both of which are considerably larger when computed using
the clover action than with the Wilson action. For example for the ratio
$f^{-1}_{J/\psi}/f^{-1}_{\rho}$ we find 0.32\err{1}{2} with the Wilson action
and $0.48\pm 3$ with the clover action (the physical value is 0.44(2)).


title:
Fast vectorized algorithm for the Monte Carlo Simulation of the Random
  Field Ising Model

abstract:
  An algoritm for the simulation of the 3--dimensional random field Ising model
with a binary distribution of the random fields is presented. It uses
multi-spin coding and simulates 64 physically different systems simultaneously.
On one processor of a Cray YMP it reaches a speed of 184 Million spin updates
per second. For smaller field strength we present a version of the algorithm
that can perform 242 Million spin updates per second on the same machine.


title:
The confined-deconfined Interface Tension and the Spectrum of the
  Transfer Matrix

abstract:
  The reduced tension $\sigma_{cd}$ of the interface between the confined and
the deconfined phase of $SU(3)$ pure gauge theory is related to the finite size
effects of the first transfer matrix eigenvalues. A lattice simulation of the
transfer matrix spectrum at the critical temperature $T_c = 1/L_t$ yields
$\sigma_{cd} = 0.139(4) T_c^2$ for $L_t = 2$. We found numerical evidence that
the deconfined-deconfined domain walls are completely wet by the confined
phase, and that the confined-deconfined interfaces are rough.


title:
Spectroscopy, Equation Of State And Monopole Percolation In Lattice QED
  With Two Flavors

abstract:
  Non-compact lattice QED with two flavors of light dynamical quarks is
simulated on $16^4$ lattices, and the chiral condensate, monopole density and
susceptibility and the meson masses are measured. Data from relatively high
statistics runs at relatively small bare fermion masses of 0.005, 0.01, 0.02
and 0.03 (lattice units) are presented. Three independent methods of data
analysis indicate that the critical point occurs at $\beta =0.225(5)$ and that
the monopole condensation and chiral symmetry breaking transitions are
coincident. The monopole condensation data satisfies finite size scaling
hypotheses with critical indices compatible with four dimensional percolation.
The best chiral equation of state fit produces critical exponents
($\delta=2.31$, $\beta_{mag}=0.763$) which deviate significantly from mean
field expectations. Data for the ratio of the sigma to pion masses produces an
estimate of the critical index $\delta$ in good agreement with chiral
condensate measurements. In the strong coupling phase the ratio of the meson
masses are $M_\sigma^2/M_\rho^2\approx 0.35$, $M_{A_1}^2/M_\rho^2\approx 1.4$
and $M_\pi^2/M_\rho^2\approx 0.0$, while on the weak coupling side of the
transition $M_\pi^2/M_\rho^2\approx 1.0$, $M_{A_1}^2/M_\rho^2\approx 1.0$,
indicating the restoration of chiral symmetry.\footnote{$\,^{}$}{August 1992}


title: Four - Fermi Theories in Fewer Than Four Dimensions

abstract:
  Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable
renormalization group fixed point at a strong value of the coupling constant
where chiral symmetry is spontaneously broken. The resulting field theory
describes relativistic fermions interacting non-trivially via exchange of
scalar bound states. We calculate the $O(1/N_f)$ corrections to this picture,
where $N_f$ is the number of fermion species, for a variety of models and
confirm their renormalizability to this order. A connection between
renormalizability and the hyperscaling relations between the theory's critical
exponents is made explicit. We present results of extensive numerical
simulations of the simplest model for $d=3$, performed using the hybrid Monte
Carlo algorithm on lattice sizes ranging from $8^3$ to $24^3$. For $N_f=12$
species of massless fermions we confirm the existence of a second order phase
transition where chiral symmetry is spontaneously broken. Using both direct
measurement and finite size scaling arguments we estimate the critical
exponents $\beta$, $\gamma$, $\nu$ and $\delta$. We also investigate symmetry
restoration at non-zero temperature, and the scalar two-point correlation
function in the vicinity of the bulk transition. All our results are in
excellent agreement with analytic predictions, and support the contention that
the $1/N_f$ expansion is accurate for this class of models.


title: Mixed Model of Induced QCD

abstract:
  The problems with the $Z_N$ symmetry breaking in the induced QCD are
analyzed. We compute the Wilson loops in the strong coupling phase, but we do
not find the $Z_N$ symmetry breaking, for arbitrary potential. We suggest to
bypass this problem by adding to the model a heavy fermion field in a
fundamental representation of $ SU(N) $. Remarkably, the model still can be
solved exactly by the Rieman-Hilbert method, for arbitrary number $N_f$ of
flavors. At $ N_f \ll N \rightarrow \infty $ there is a new regime, with two
vacuum densities. The $Z_N$ symmetry breaking density satisfies the linear
integral equation, with the kernel, depending upon the old density. The
symmetry breaking requires certain eigenvalue condition, which takes some extra
parameter adjustment of the scalar potential.


title: Finite-Size Scaling on the Ising Coexistence Line

abstract:
  We report tests of finite-size scaling ansatzes in the low temperature phase
of the two-dimensional Ising model. For moments of the magnetisation density,
we find good agreement with the new ansatz of Borgs and Koteck\'y, and clear
evi consequences of the convexity of the free energy are not adequately treated
in either of these approaches.\lb {\it Keywords}\/: Finite-size scaling, 2-d
Ising, pure-phase susceptibility.


title: Decuplet Baryon Structure from Lattice QCD

abstract:
  The electromagnetic properties of the SU(3)-flavor baryon decuplet are
examined within a lattice simulation of quenched QCD. Electric charge radii,
magnetic moments, and magnetic radii are extracted from the E0 and M1 form
factors. Preliminary results for the E2 and M3 moments are presented giving the
first model independent insight to the shape of the quark distribution in the
baryon ground state. As in our octet baryon analysis, the lattice results give
evidence of spin-dependent forces and mass effects in the electromagnetic
properties. The quark charge distribution radii indicate these effects act in
opposing directions. Some baryon dependence of the effective quark magnetic
moments is seen. However, this dependence in decuplet baryons is more subtle
than that for octet baryons. Of particular interest are the lattice predictions
for the magnetic moments of $\Omega^-$ and $\Delta^{++}$ for which new recent
experimental measurements are available. The lattice prediction of the
$\Delta^{++}/p$ ratio appears larger than the experimental ratio, while the
lattice prediction for the $\Omega^-/p$ magnetic moment ratio is in good
agreement with the experimental ratio.


title: Numerical Study of Finite Size Scaling for First Order Phase Transitions

abstract:
  I present results of simulations of the q=10 and q=20 2-d Potts models in the
transition region. The asymptotic finite size behavior sets in only for
extremely large lattices. We learn from this simulation that finite size
scaling cannot be used to decide that a transition is first order.


title:
Non-perturbative analysis, Gribov horizons and the boundary of the
  fundamental domain

abstract:
  In this contribution to the proceedings we will describe some of the details
for constructing the Gribov horizon and the boundary of the fundamental modular
domain, when restricting to some low energy modes of pure SU(2) gauge theory in
a spherical spatial geometry. The fundamental domain is a one-to-one
representation of the set of gauge invariant degrees of freedom, in terms of
transverse gauge fields. Boundary identifications are the only remnants of the
Gribov copies.


title: Running Coupling and the Lambda-Parameter from SU(3) Lattice Simulations

abstract:
  We present new results on the static qq-potential from high statistics
simulations on 32^4 and smaller lattices, using the standard Wilson beta = 6.0,
6.4, and 6.8. Within our statistical errors we do not observe any finite size
effects affecting the potential values, on varying the spatial lattice extent
from 0.9fm up to 3.3fm. We are able to see and quantify the running of the
coupling from the Coulomb behaviour of the interquark force. From this we
extract the ratio \sqrt{sigma}/Lambda_L. We demonstrate that scaling violations
on the string tension can be considerably reduced by introducing effective
coupling schemes, which allow for a safe extrapolation of \Lambda_L to its
continuum value. Both methods yield consistent values for Lambda: Lambda_MSbar
= 0.558_{-0.007}^{+0.017}\sqrt{sigma} = 246_{-3}^{+7}MeV. At the highest energy
scale attainable to us we find alpha(5 GeV) = 0.150(3)


title: A Study of the $N=2$ Kazakov-Migdal Model

abstract:
  We study numerically the SU(2) Kazakov-Migdal model of `induced QCD'. In
contrast to our earlier work on the subject we have chosen here {\it not} to
integrate out the gauge fields but to keep them in the Monte Carlo simulation.
This allows us to measure observables associated with the gauge fields and
thereby address the problem of the local $Z_2$ symmetry present in the model.
We confirm our previous result that the model has a line of first order phase
transitions terminating in a critical point. The adjoint plaquette has a clear
discontinuity across the phase transition, whereas the plaquette in the
fundamental representation is always zero in accordance with Elitzur's theorem.
The density of small $Z_2$ monopoles shows very little variation and is always
large. We also find that the model has extra local U(1) symmetries which do not
exist in the case of the standard adjoint theory. As a result, we are able to
show that two of the angles parameterizing the gauge field completely decouple
from the theory and the continuum limit defined around the critical point can
therefore not be `QCD'.


title: Lattice Calculation of QCD Vacuum Correlation Functions

abstract:
  The first exploratory calculations of QCD vacuum correlation functions on a
lattice are reported. Qualitative agreement with phenomenological results is
obtained in channels for which experimental data are available, and these
correlation functions are shown to be useful in exploring approximations based
on sum rules and interacting instantons.


title: Asymptotic Freedom and Euclidean Quantum Gravity

abstract:
  Pure SU(2) gauge theory is the simplest asymptotically free theory in four
dimensions. To investigate Euclidean quantum gravity effects in a fundamental
length scenario, we simulate 4$d$ SU(2) lattice gauge theory on a dynamically
coupled Regge skeleton. The fluctuations of the skeleton are governed by the
standard Regge-Einstein action. From a small $2\cdot 4^3$ lattice we report
exploratory numerical results, limited to a region of strong gravity where the
Planck mass and hadronic masses take similar orders of magnitude. We find a
range of the Planck mass where stable bulk expectation values are obtained
which vary smoothly with the gauge coupling, and a remnant of the QCD
deconfining phase transition is located. Note: The full ps file of this
preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps
file, ftp to this address and use for username "anonymous" and for password
your name. The file is in the directory pub/krishnan (to go to that directory
type: cd pub/krishnan) and is called gravity.ps (to get it type: get
gravity.ps). If you have any problems send mail to krishnan@ds1.scri.fsu.edu.


title: Critical Momenta of Lattice Chiral Fermions

abstract:
  We determine the critical momenta for chiral fermions in the domain wall
model recently suggested by Kaplan. For a wide range of domain wall masses $m$
and Wilson couplings $r$ we explicitly exhibit the regions in momentum space
where the fermions are chiral. We compare the critical momenta for the
infinitely large system with those obtained on a finite lattice.


title: Chern-Simons Currents and Chiral Fermions on the Lattice

abstract:
  We compute the Chern-Simons current induced by Wilson fermions on a $d=2n+1$
dimensional lattice, making use of a topological interpretation of the momentum
space fermion propagator as a map from the torus to the sphere, $T^{d}\to
S^{d}$. These mappings are shown to fall in different homotopy classes
depending on the value of $m/r$, where $m$ is the fermion mass and $r$ is the
Wilson coupling. As a result, the induced Chern-Simons term changes
discontinuously at $d+1$ different values for $m$, unlike in the continuum.
This behavior is exactly what is required by the peculiar spectrum found for a
recently proposed model of chiral lattice fermions as zeromodes bound to a
domain wall.


title: The Finite Temperature Phase Diagram of a U(1) Higgs-Yukawa Model

abstract:
  The finite temperature phase diagram of a U(1) Higgs-Yukawa model at a finite
value of the scalar self coupling $\lambda$ is investigated by means of a
large-$N_f$ calculation and numerical simulations. The phase diagram is similar
to the one at zero temperature and shows a ferromagnetic, two symmetric and an
antiferromagnetic phase. However, the phase transition lines are shifted to
larger values of the Yukawa coupling demonstrating the occurence of the finite
temperature symmetry restoration.


title: High Precision Simulation Techniques for Lattice Field Theory

abstract:
  An overview is given over the recently developed and now widely used Monte
Carlo algorithms with reduced or eliminated critical slowing down. The basic
techniques are overrelaxation, cluster algorithms and multigrid methods. With
these tools one is able to probe much closer than before the universal
continuum behavior of field theories on the lattice.


title: Capillary Waves in Binder's Approach to the Interface Tension

abstract:
  In Binder's approach the reduced interface tension sigma of the Ising model
in the broken phase is determined from the finite volume effects of the
partition function Z(M) at fixed total magnetization M. For small |M| the
partition function of a system of size L^d with periodic boundary conditions is
dominated by configurations with two interfaces, such that Z(M) ~ exp(- 2 sigma
L^{d-1}). Capillary wave fluctuations of the interfaces correct this result to
Z(M) ~ exp(- 2 sigma L^{d-1}) with x = -1. The knowledge of the pre-exponential
behavior allows an improved fit of numerical data, and a determination of the
interface stiffness.


title: SU(2) Potentials from Large Lattices

abstract:
  We measure accurate values of the inter-quark potentials on a $48^{3}56$
lattice with SU(2) pure gauge theory at $ \beta =2.85$. The scale is set by
extracting the string tension - we obtain ${\sqrt K}a=0.063(3)$ at $\beta
=2.85.$ From a careful study of the small-$R$ potentials in the region 2 GeV $<
R^{-1} < 5$ GeV, we extract a running coupling constant and estimate the scale
$\Lambda _{\msbar} = 272(24)$ MeV.


title: The Running Coupling from SU(3) Lattice Gauge Theory

abstract:
  {}From an accurate determination of the inter-quark potential, one can study
the running coupling constant for a range of $R$-values and hence estimate the
scale $\Lambda_{\msbar} $. Detailed results are presented for $SU(3)$ pure
gauge theory.


title:
Monopole Percolation and The Universality Class of the Chiral Transition
  in Four Flavor Noncompact Lattice QED

abstract:
  We simulate four flavor noncompact lattice QED using the Hybrid Monte Carlo
algorithm on $10^4$ and $16^4$ lattices. Measurements of the monopole
susceptibility and the percolation order parameter indicate a transition at
$\beta = {1/e^2} = .205(5)$ with critical behavior in the universality class of
four dimensional percolation. We present accurate chiral condensate
measurements and monitor finite size effects carefully. The chiral condensate
data supports the existence of a power-law transition at $\beta = .205$ in the
same universality class as the chiral transition in the two flavor model. The
resulting equation of state predicts the mass ratio $m_\pi^2/m_\sigma^2$ in
good agreement with spectrum calculations while the hypothesis of a
logarithmically improved mean field theory fails qualitatively.


title: Universal Properties of Chiral Simmetry Breaking

abstract:
  We discuss chiral symmetry breaking critical points from the perspective of
PCAC, correlation length scaling and the chiral equation of state. A scaling
theory for the ratio $R_\pi$ of the pion to sigma masses is presented. The
Goldstone character of the pion and properties of the longitudinal and
transverse chiral susceptibilities determine the ratio $R_\pi$ which can be
used to locate critical points and measure critical indices such as $\delta$.
We show how PCAC and correlation length scaling determine the pion mass'
dependence on the chiral condensate and lead to a practical method to measure
the anomalous dimension $\eta$. These tools are proving useful in studies of
the chiral transition in lattice QED and the quark-gluon plasma transition in
lattice QCD.


title:
A quantitative study of the Kosterlitz-Thouless phase transition in a
  system of two-dimensional plane rotators ( XY model ) by high temperature
  expansions through $\beta^{20}$

abstract:
  High temperature series expansions of the spin-spin correlation function for
the plane rotator (or XY) model on the square lattice are extended by three
terms through order $\beta^{20}$. Tables of the expansion coefficients are
reported for the correlation function spherical moments of order $l=0,1,2$. The
expansion coefficients through $\beta^{15}$ for the vorticity are also
tabulated. Our analysis of the series supports the Kosterlitz-Thouless
predictions on the structure of the critical singularities and leads to fairly
accurate estimates of the critical parameters.


title:
Rotational Symmetry and Regularization Dependence in the
  $\Phi^4_4$-Model

abstract:
  We study the one component $\Phi^4$ model for four different lattice actions
in the Gaussian limit and for the Ising model in the broken phase. Emphasis is
put on the euclidean invariance properties of the boson propagator. A measure
of the violation of rotational symmetry serves as a tool to compare the
regularization dependence of the triviality bound.


title:
Surface Tension, Surface Stiffness, and Surface Width of the
  3-dimensional Ising Model on a Cubic Lattice

abstract:
  We compute properties of the interface of the 3-dimensional Ising model for a
wide range of temperatures, covering the whole region from the low temperature
domain through the roughening transition to the bulk critical point. The
interface tension sigma is obtained by integrating the surface energy density
over the inverse temperature beta. We use lattices of size L x L x T, with L up
to 64, and T up to 27. The simulations with antiperiodic boundary conditions in
T-direction are done with the Hasenbusch-Meyer interface cluster algorithm that
turns out to be very efficient. We demonstrate that in the rough phase the
large distance behavior of the interface is well described by a massless
Gaussian dynamics. The surface stiffness coefficient kappa is determined. We
also attempt to determine the correlation length xi and study universal
quantities like xi^2 * sigma and xi^2 * kappa. Results for the interfacial
width on lattices up to 512 x 512 x 27 are also presented.


title: Glueballs and Hybrid Mesons

abstract:
  We discuss states in the meson spectrum which have explicit gluonic
components. Glueballs (with no valence quarks) and hybrid mesons (with valence
quarks) are both reviewed. We present in some detail lattice simulation
results. ( to appear in proceedings of QCD-20 years, Aachen Workshop)


title: Chern-Simons term and Topological Charge on the Lattice

abstract:
  In a somewhat overlooked work by Seiberg, a definition of the topological
charge for SU(N) lattice fields was given. Here, it is shown that Seibergs and
L\"{u}schers charge definition are related up to the section of the bundle.
With the continued interest in baryon number violating processes, Seibergs
paper is useful since it allows for a Chern-Simons number also.


title: Direct Monte Carlo Measurement of the Surface Tension in Ising Models

abstract:
  I present a cluster Monte Carlo algorithm that gives direct access to the
interface free energy of Ising models. The basic idea is to simulate an
ensemble that consists of both configurations with periodic and with
antiperiodic boundary conditions. A cluster algorithm is provided that
efficently updates this joint ensemble. The interface tension is obtained from
the ratio of configurations with periodic and antiperiodic boundary conditions,
respectively. The method is tested for the 3-dimensional Ising model.


title:
Finite-Size Scaling Study of the Three-Dimensional Classical Heisenberg
  Model

abstract:
  We use the single-cluster Monte Carlo update algorithm to simulate the
three-dimensional classical Heisenberg model in the critical region on simple
cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By
means of finite-size scaling analyses we compute high-precision estimates of
the critical temperature and the critical exponents, using extensively
histogram reweighting and optimization techniques. Measurements of the
autocorrelation time show the expected reduction of critical slowing down at
the phase transition. This allows simulations on significantly larger lattices
than in previous studies and consequently a better control over systematic
errors in finite-size scaling analyses.


title: Lyapunov Exponent of SU(3) Gauge Theory

abstract:
  The classical SU(3) gauge theory is shown to be deterministic chaotic. Its
largest Lyapunov exponent is dertermined, from which a short time scale of
thermalization of a pure gluon system is estimated. The connection to gluon
damping rate is discussed.


title: Multi-quark energies in QCD

abstract:
  Four-quark potentials for $SU(2)$ are evaluated in the static limit with the
quenched approximation -- using a lattice of $16^3\times 32$ and $\beta=2.4$.
The four quarks are restricted to the corners of rectangles with sides upto
seven lattice spacings long. The results are analysed in terms of a strategy
based on interquark two-body potentials -- as advocated earlier by the authors.
This shows that a standard two-body approach overestimates the four-quark
binding energy by upto a factor of about three for the largest rectangles.


title: The Phase Diagram of Fluid Random Surfaces with Extrinsic Curvature

abstract:
  We present the results of a large-scale simulation of a Dynamically
Triangulated Random Surface with extrinsic curvature embedded in
three-dimensional flat space. We measure a variety of local observables and use
a finite size scaling analysis to characterize as much as possible the regime
of crossover from crumpled to smooth surfaces.


title: Neural multigrid for gauge theories and other disordered systems

abstract:
  We present evidence that multigrid works for wave equations in disordered
systems, e.g. in the presence of gauge fields, no matter how strong the
disorder, but one needs to introduce a "neural computations" point of view into
large scale simulations: First, the system must learn how to do the simulations
efficiently, then do the simulation (fast).
  The method can also be used to provide smooth interpolation kernels which are
needed in multigrid Monte Carlo updates.


title: On the Viability of Lattice Perturbation Theory

abstract:
  In this paper we show that the apparent failure of QCD lattice perturbation
theory to account for Monte Carlo measurements of perturbative quantities
results from choosing the bare lattice coupling constant as the expansion
parameter. Using instead ``renormalized'' coupling constants defined in terms
of physical quantities, like the heavy-quark potential, greatly enhances the
predictive power of lattice perturbation theory. The quality of these
predictions is further enhanced by a method for automatically determining the
coupling-constant scale most appropriate to a particular quantity. We present a
mean-field analysis that explains the large renormalizations relating lattice
quantities, like the coupling constant, to their continuum analogues. This
suggests a new prescription for designing lattice operators that are more
continuum-like than conventional operators. Finally, we provide evidence that
the scaling of physical quantities is asymptotic or perturbative already at
$\beta$'s as low as 5.7, provided the evolution from scale to scale is analyzed
using renormalized perturbation theory. This result indicates that reliable
simulations of (quenched) QCD are possible at these same low $\beta$'s.


title: Modified $U(1)$ lattice gauge theory: towards realistic lattice QED

abstract:
  We study properties of the compact $~4D~$ $U(1)$ lattice gauge theory with
monopoles {\it removed}. Employing Monte Carlo simulations we calculate
correlators of scalar, vector and tensor operators at zero and nonzero momenta
$~\vec{p}~$. We confirm that the theory without monopoles has no phase
transition, at least, in the interval $~0 < \beta \leq 2~$. There the photon
becomes massless and fits the lattice free field theory dispersion relation
very well. The energies of the $~0^{++}~$, $~1^{+-}~$ and $~2^{++}~$ states
show a rather weak dependence on the coupling in the interval of $~\beta~$
investigated, and their ratios are practically constant. We show also a further
modification of the theory suppressing the negative plaquettes to improve
drastically the overlap with the lowest states (at least, for $~J=1$).


title: Multicanonical Cluster Algorithm and the 2-D 7-State Potts Model

abstract:
  I present a hybrid-like two-step algorithm, which combines a microcanonical
update of a spin system using demons, with a multicanonical demon refresh. The
algorithm is free from the supercritical slowing down that burdens the
canonical methods: the exponential increase of the tunnelling time between the
metastable states in the first-order phase transitions, when the volume of the
system is increased. The demons act as a buffer between the multicanonical heat
bath and the spin system, allowing the spin system to be updated with any
microcanonical demon procedure, including cluster methods. The cluster
algorithm is demonstrated with the 2-dimensional 7-state Potts model, using
volumes up to $128^2$. The tunnelling time is found to increase as $L^{1.82}$,
where $L$ is the linear dimension of the system.


title: Monte Carlo simulation of lattice ${\rm CP}^{N-1}$ models at large N

abstract:
  In order to check the validity and the range of applicability of the 1/N
expansion, we performed numerical simulations of the two-dimensional lattice
CP(N-1) models at large N, in particular we considered the CP(20) and the
CP(40) models. Quantitative agreement with the large-N predictions is found for
the correlation length defined by the second moment of the correlation
function, the topological susceptibility and the string tension. On the other
hand, quantities involving the mass gap are still far from the large-$N$
results showing a very slow approach to the asymptotic regime. To overcome the
problems coming from the severe form of critical slowing down observed at large
N in the measurement of the topological susceptibility by using standard local
algorithms, we performed our simulations implementing the Simulated Tempering
method.


title:
Bose Condensation and $Z_N$ Symmetry Breaking in the Mixed Model of
  Induced QCD

abstract:
  The mixed model of the large $ N $ induced QCD, with $ N_f \ll N $ flavors of
heavy fermions in fundamental representation, is solved in the local limit. The
$ Z_N$ symmetry is broken spontaneously in the large $ N $ limit, evading the
Elitzur "no-go" theorem. As a result of this symmetry breaking, there is the
Bose condensate of the eigenvalues of the scalar field, proportional to $
\frac{N_f}{N} $. This condensate leads to the mass unit, which goes to zero as
fractional power of $ \frac{N_f}{N} $, thus defining the new kind of the local
limit of this lattice theory. There is a strong coupling region below this mass
scale, which revives the hopes of induction of realistic QCD.


title: Chern-Simons term in the 4-dimensional SU(2) Higgs Model

abstract:
  Using Seiberg's definition for the geometric charge in SU(2) lattice gauge
theory, we have managed to apply it also to the Chern-Simons term. We checked
the periodic structure and determined the Chern-Simons density on small
lattices $L^4$ and $L^3 \times 2,\, 4$ with $L=4,\, 6,\mbox{ and }8$ near the
critical region in the SU(2) Higgs model. The data indicate that tunneling is
increased at high temperature.


title: Non-uniform measure in 4d simplicial quantum gravity

abstract:
  Four-dimensional euclidean quantum gravity has been studied as a discrete
model based on dynamical triangulations by Ambjorn and Jurkiewicz and by
Agishtein and Migdal. We discuss a particular implementation of a Monte Carlo
simulation of simplicial quantum gravity. As an application we introduce a
non-uniform measure and examine its effect on simple aspects of the
mathematical geometry. We find that the transition region from the hot to the
cold phase is shifted and that the criticality of the transition changes.


title: 4d Simplicial Quantum Gravity with a Non-Trivial Measure

abstract:
  We study 4d simplicial quantum gravity in the dynamical triangulation
approach with a non-trivial class of measures. We find that the measure
contribution plays an important role, influencing the phase diagram and the
nature of the (possible) critical theory. We discuss how the lattice theory
could be used to fix the quantum measure in a non-ambiguous way.


title: The Running Coupling from SU(3) Gauge Theory

abstract:
  We present high precision results on the static quark-antiquark-potential on
32^4 and smaller lattices, using the standard Wilson action at BETA = 6.0, 6.2,
6.4, and 6.8 on the Connection Machine CM-2. Within our statistical errors (1%)
we did not observe any finite size effects affecting the potential values, on
varying the spatial lattice extent from 0.9 fm up to 3.3 fm. We find violations
of asymptotic scaling in the bare coupling up to BETA = 6.8. We demonstrate
that scaling violations on the string tension can be considerably reduced by
introducing effective coupling schemes, which allow for a safer extrapolation
of LAMBDA_Lattice to its continuum value. We are also able to see and to
quantify the running of the coupling from the interquark force. From this we
extract the ratio \sqrt{SIGMA}/LAMBDA_L. Both methods yield consistent values
for the LAMBDA-parameter: LAMBDA_MSbar = 0.558(-0.007+0.017)\sqrt{SIGMA}
  = 246(-3+7) MeV.


title:
Multicritical Points in a Lattice Yukawa Model with the Wilson-Yukawa
  Coupling

abstract:
  For a lattice regularized chiral-invariant $SU(2)_L\times~SU(2)_R$
fermion-scalar model with a Yukawa coupling $y$ and a Wilson-Yukawa coupling
$w$, we investigate the phase structure and in particular show the existence of
the multicritical line, in the strong Yukawa and/or Wilson Yukawa coupling
region, at which four phases meet.
  The result is in good agreement with the Monte Carlo simulation.
  This analytical result is derived from the effective scalar model obtained by
integrating out the fermion field where the action is explicitly obtained from
the hopping parameter expansion up to next-to-leading order.
  For estimates on the correlation function of the scalar field we apply the
mean-field method.


title: Fermion Doubling and Gauge Invariance on Random Lattices

abstract:
  Random-lattice fermions have been shown to be free of the doubling problem if
there are no interactions or interactions of a non-gauge nature. On the other
hand, gauge interactions impose stringent constraints as expressed by the
Ward-Takahashi identities which could revive the free-field suppressed doubler
modes in loop diagrams. Comparing random lattice, naive and Wilson fermions in
two dimensional abelian background gauge theory, we show that indeed the
doublers are revived for random lattices in the continuum limit. Some
implications of the persistent doubling phenomenon on random lattices are also
discussed.


title: Basis States for Hamiltonian QCD with Dynamical Quarks

abstract:
  We discuss the construction of basis states for Hamiltonian QCD on the
lattice, in particular states with dynamical quark pairs. We calculate the
matrix elements of the operators in the QCD Hamiltonian between these states.
Along with the ``harmonic oscillator'' states introduced in previous pure SU(3)
work, these states form a working basis for calculations in full QCD.


title: The infrared limit of QCD effective string

abstract:
  Some model-independent properties of the effective string of gauge field
systems in the confining phase , for very large quark separations, are
described in terms of two-dimensional conformal field theories. The constraints
induced by the gauge theory at the boundaries of the effective string induce a
Coulomb- like term in the interquark potential which is universal, but
different from the one proposed by L\"uscher. Some universal relations among
the string tension, the thickness of the colour flux tube, the location of the
deconfining temperature and a lower bound of the glueball spectrum are
discussed. (Lectures given at the XXXII Cracow School of Theoretical Physics,
Zakopane, Poland 2-12 June 1992)


title:
SU(N) Gauge Theories with C-Periodic Boundary Conditions: II. Small
  Volume Dynamics

abstract:
  The dynamics of SU(N) gauge theories, especially for N=3, in a small
C-periodic box are investigated. We identify the fields that mimimize the
energy---the torons---and determine which of these ``classical'' vacua are
stable quantum mechanically. The stable torons break cubic symmetry, which has
interesting consequences on the spectrum. At any of the stable torons there are
also quartic modes. Since all C-periodic boundary conditions are
gauge-equivalent, we choose a convenient version, for which the quartic modes
are constant modes, and compute the effective Hamiltonian to one loop in
perturbation theory.


title:
Renormalization Group Analysis of Finite-Size Scaling in the $\Phi^4_4$
  Model

abstract:
  A finite-size scaling theory for the $\phi^4_4$ model is derived using
renormalization group methods. Particular attention is paid to the partition
function zeroes, in terms of which all thermodynamic observables can be
expressed. While the leading scaling behaviour is identical to that of mean
field theory, there exist multiplicative logarithmic corrections too. A
non-perturbative test of these formulae in the form of a high precision Monte
Carlo analysis reveals good quantitative agreement with the analytical
predictions.


title: Scaling and asymptotic scaling in two-dimensional $CP^{N-1}$ models

abstract:
  Two-dimensional $CP^{N-1}$ models are investigated by Monte Carlo methods on
the lattice, for values of $N$ ranging from 2 to 21. Scaling and rotation
invariance are studied by comparing different definitions of correlation length
$\xi$. Several lattice formulations are compared and shown to enjoy scaling for
$\xi$ as small as $2.5$. Asymptotic scaling is investigated using as bare
coupling constant both the usual $\beta$ and $\beta_E$ (related to the internal
energy); the latter is shown to improve asymptotic scaling properties. Studies
of finite size effects show their $N$-dependence to be highly non-trivial, due
to the increasing radius of the $\bar z z$ bound states at large $N$.


title: $1/N$ Expansion of Two-Dimensional Models in the Scaling Region

abstract:
  The main technical and conceptual features of the lattice $1/N$ expansion in
the scaling region are discussed in the context of a two-parameter
two-dimensional spin model interpolating between $CP^{N-1}$ and $O(2N)$
$\sigma$ models, with standard and improved lattice actions. We show how to
perform the asymptotic expansion of effective propagators for small values of
the mass gap and how to employ this result in the evaluation of physical
quantities in the scaling regime. The lattice renormalization group $\beta$
function is constructed explicitly and exactly to $O({1/N})$.


title: Topological susceptibility and string tension in CP(N-1) models

abstract:
  We investigate the features of ${\rm CP}^{N-1}$ models concerning confinement
and topology. In order to study the approach to the large-$N$ asymptotic
regime, we determine the topological susceptibility and the string tension for
a wide range of values of $N$, in particular $N=4,10,21,41$. Quantitative
agreement with the large-$N$ predictions is found for the ${\rm CP}^{20}$ and
the ${\rm CP}^{40}$ models. Problems related to the measure of the topological
susceptibility and the string tension on the lattice are discussed.


title: Wave functions and their use in spectroscopy and phenomenology

abstract:
  We describe the calculation of Coulomb gauge wave functions for light quark
systems, and their use as interpolating fields for excited state spectroscopy.


title: The U(1)-Higgs Model: Critical Behaviour in the Confinig-Higgs region

abstract:
  We study numerically the critical properties of the U(1)-Higgs lattice model,
with fixed Higgs modulus, in the region of small gauge coupling where the Higgs
and Confining phases merge. We find evidence of a first order transition line
that ends in a second order point. By means of a rotation in parameter space we
introduce thermodynamic magnitudes and critical exponents in close resemblance
with simple models that show analogous critical behaviour. The measured data
allow us to fit the critical exponents finding values in agreement with the
mean field prediction. The location of the critical point and the slope of the
first order line are accurately given.


title: The nature of the continuum limit in strongly coupled quenched QED

abstract:
  We review the results of large scale simulations of noncompact quenched $QED$
which use spectrum and Equation of State calculations to determine the theory's
phase diagram, critical indices, and continuum limit. The resulting anomalous
dimensions are in good agreement with Schwinger-Dyson solutions of the ladder
graphs of conventional $QED$ and they satisfy the hyperscaling relations
expected of a relativistic renormalizable field theory. The spectroscopy
results satisfy the constraints of the Goldstone mechanism and PCAC, and may be
indicative of Technicolor versions of the Standard Model which are strongly
coupled at short distances.


title:
Improvement of efficiency in generating random $U(1)$ variables with
  Boltzmann distribution

abstract:
  A method for generating random $U(1)$ variables with Boltzmann distribution
is presented. It is based on the rejection method with transformation of
variables. High efficiency is achieved for all range of temparatures or
coupling parameters, which makes the present method especially suitable for
parallel and pipeline vector processing machines. Results of computer runs are
presented to illustrate the efficiency. An idea to find such algorithms is also
presented, which may be applicable to other distributions of interest in Monte
Carlo simulations.


title: Lee-Yang Zeroes and Logarithmic Corrections in the $\Phi^4_4$ Theory

abstract:
  The leading mean-field critical behaviour of $\phi^4_4$-theory is modified by
multiplicative logarithmic corrections. We analyse these corrections both
analytically and numerically. In particular we present a finite-size scaling
theory for the Lee-Yang zeroes and temperature zeroes, both of which exhibit
logarithmic corrections. On lattices from size $8^4$ to $24^4$, Monte-Carlo
cluster methods and multi-histogram techniques are used to determine the
partition function zeroes closest to the critical point. Finite-size scaling
behaviour is verified and the logarithmic corrections are found to be in good
agreement with our analytical predictions.


title: The Kaon $B$-parameter with Wilson Fermions

abstract:
  We calculate the kaon $B$-parameter in quenched lattice QCD at $\beta=6.0$
using Wilson fermions at $\kappa=0.154$ and $0.155$. We use two kinds of
non-local (``smeared'') sources for quark propagators to calculate the matrix
elements between states of definite momentum. The use of smeared sources yields
results with much smaller errors than obtained in previous calculations with
Wilson fermions. By combining results for $\vec p =(0,0,0)$ and $\vec p
=(0,0,1)$, we show that one can carry out the non-perturbative subtraction
necessary to remove the dominant lattice artifacts induced by the chiral
symmetry breaking term in the Wilson action. Our final results are in good
agreement with those obtained using staggered fermions. We also present results
for $B$-parameters of the $\Delta I = 3/2$ part of the electromagnetic penguin
operators, and preliminary results for \bk\ in the presence of two flavors of
dynamical quarks.


title: Bosonization and Cluster Updating of Lattice Fermions

abstract:
  A lattice fermion model is formulated in Fock space using the Jordan-Wigner
representation for the fermion creation and annihilation operators. The
resulting path integral is a sum over configurations of lattice site occupation
numbers $n(x,t) = 0,1$ which may be viewed as bosonic Ising-like variables.
However, as a remnant of Fermi statistics a nonlocal sign factor arises for
each configuration. When this factor is included in measured observables the
bosonic occupation numbers interact locally, and one can use efficient cluster
algorithms to update the bosonized variables.


title: Intermittency Studies in Directed Bond Percolation

abstract:
  The self-similar cluster fluctuations of directed bond percolation at the
percolation threshold are studied using techniques borrowed from
inter\-mit\-ten\-cy-related analysis in multi-particle production. Numerical
simulations based on the factorial moments for large $1+1$-dimensional lattices
allow to handle statistical and boundary effects and show the existence of weak
but definite intermittency patterns. The extracted fractal dimensions are in
agreement with scaling arguments leading to a new relation linking the
intermittency indices to the critical exponents and the fractal dimension of
directed percolation clusters.


title:
The String Tension in Gauge Theories: a Suggestion for a New Measurement
  Method

abstract:
  We discuss a new method for testing confinement and measuring the string
tension (in the Coulomb gauge). Our numerical simulations demonstrate that the
problems related to Gribov copies are not harmful and that the method is
effective in the case of pure gauge Q.C.D.. We discuss the relevance of the
method for studying gauge theories coupled to fermionic matter.


title: Fermion-Higgs model with strong Wilson-Yukawa coupling in two dimensions

abstract:
  The fermion mass spectrum is studied in the quenched approximation in the
strong coupling vortex phase (VXS) of a globally U(1)$_L \otimes$U(1)$_R$
symmetric scalar-fermion model in two dimensions. In this phase fermion
doublers can be completely removed from the physical spectrum by means of a
strong Wilson-Yukawa coupling. The lowest lying fermion spectrum in this phase
consists most probably only of a massive Dirac fermion which has charge zero
with respect to the $U(1)_L$ group. We give evidence that the fermion which is
charged with respect to that subgroup is absent in the VXS phase. When the
$U(1)_L$ gauge fields are turned on, the neutral fermion may couple chirally to
the massive vector boson state in the confinement phase. The outcome is very
similar to our findings in the strong coupling symmetric phase (PMS) of
fermion-Higgs models with Wilson-Yukawa coupling in four dimensions, with the
exception that in four dimensions the neutral fermion does most probably
decouple from the bosonic bound states.


title: Scattering in a Simple 2-d Lattice Model

abstract:
  L\"uscher has suggested a method to determine phase shifts from the finite
volume dependence of the two-particle energy spectrum. We apply this to two
models in d=2: (a) the Ising model, (b) a system of two Ising fields with
different mass and coupled through a 3-point term, both considered in the
symmetric phase. The Monte Carlo simulation makes use of the cluster updating
and reduced variance operator techniques. For the Ising system we study in
particular O($a^2$) effects in the phase shift of the 2-particle scattering
process.


title:
Dual of 3-dimensional pure SU(2) Lattice Gauge Theory and the
  Ponzano-Regge Model

abstract:
  By carrying out character expansion and integration over all link variables,
the partition function of 3-dimensional pure SU(2) lattice gauge theory is
rewritten in terms of 6j symbols. The result is Ponzano-Regge model of
3-dimensional gravity with a term that explicitly breaks general coordinate
invariance. Conversely, we show that dual of Ponzano-Regge model is an SU(2)
lattice gauge theory where all plaquette variables are constrained to the
identity matrix and therefore the model needs no further regularization. Our
techniques are applicable to other models with non-abelian symmetries in any
dimension and provide duality transform for the partition function.


title: Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo

abstract:
  We analyze the kinematics of multigrid Monte Carlo algorithms by
investigating acceptance rates for nonlocal Metropolis updates. With the help
of a simple criterion we can decide whether or not a multigrid algorithm will
have a chance to overcome critial slowing down for a given model. Our method is
introduced in the context of spin models. A multigrid Monte Carlo procedure for
nonabelian lattice gauge theory is described, and its kinematics is analyzed in
detail.


title: Regularization dependence of the Higgs mass triviality bound

abstract:
  We calculate the triviality bound on the Higgs mass in scalar field theory
models whose global symmetry group $SU(2)_L \times SU(2)_{\rm custodial}
\approx O(4)$ has been replaced by $O(N)$ and $N$ has been taken to infinity.
Limits on observable cutoff effects at four percent in several regularized
models with tunable couplings in the bare action yield triviality bounds
displaying a large degree of universality. Extrapolating from $N=\infty$ to
$N=4$ we conservatively estimate that a Higgs particle with mass up to
$0.750~TeV$ and width up to $0.290~TeV$ is realizable without large cutoff
effects, indicating that strong scalar self interactions in the standard model
are not ruled out. We also present preliminary numerical results of the
physical $N=4$ case for the $F_4$ lattice that are in agreement with the large
$N$ expectations. Note: The full ps file is also available via anonymous ftp to
ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username
"anonymous" and for password your name. The file is in the directory pub/vranas
(to go to that directory type: cd pub/vranas) and is called lat92_proc.ps (to
get it type: get lat92_proc.ps)


title:
Nonperturbative evaluation of the diffusion rate in field theory at high
  temperatures

abstract:
  Kramer's approach to the rate of the thermally activated escape from a
metastable state is extended to field theory. Diffusion rate in the
1+1-dimensional Sine-Gordon model as a function of temperature and friction
coefficient is evaluated numerically by solving the Langevin equation in real
time. A clear crossover from the semiclassical to the high temperature domain
is observed. The temperature behaviour of the diffusion rate allows one to
determine the kink mass which is found equal to the corresponding classical
value. The Kramer's predictions for the dependence on viscosity are
qualitatively valid in this multidimensional case. In the limit of vanishing
friction the diffusion rate is shown to coincide with the one obtained from the
direct measurements of the conventional classical real-time Green function at
finite temperature.


title:
The Savvidy ``ferromagnetic vacuum'' in three-dimensional lattice gauge
  theory

abstract:
  The vacuum effective potential of three-dimensional SU(2) lattice gauge
theory in an applied color-magnetic field is computed over a wide range of
field strengths. The background field is induced by an external current, as in
continuum field theory. Scaling and finite volume effects are analyzed
systematically. The first evidence from lattice simulations is obtained of the
existence of a nontrivial minimum in the effective potential. This supports a
``ferromagnetic'' picture of gluon condensation, proposed by Savvidy on the
basis of a one-loop calculation in (3+1)-dimensional QCD.


title:
Renormalisation of lattice currents and the calculation of decay
  constants for dynamical staggered fermions

abstract:
  A numerical calculation of the lattice staggered renormalisation constants at
$\beta = 5.35$, $m = 0.01$ is presented. It is seen that there are considerable
non-perturbative effects present. As an application the vector decay constant
$f_\rho$ is estimated. (LAT92 contribution, one LATEX file with 3 postscript
figures appended.)


title: Dual Superconductor Mechanism of Confinement on the Lattice

abstract:
  We investigate the dual superconductor mechanism of confinement for pure
SU(2) lattice gauge theory in the maximally abelian gauge. We focus on the the
dual Meissner effect. We find that the transverse distribution of the
longitudinal chromoelectric field due to a static quark-antiquark pair
satisfies the dual London equation. Moreover we show that the size of the flux
tube scales according to asymptotic freedom.


title:
Some universal features of the effective string picture of pure gauge
  theories

abstract:
  The effective string describing the large distance behaviour of the quark
sources of gauge field theories in the confining phase in D=3 or D=4 space-time
dimensions can be formulated, in the infrared limit, as a suitable 2D conformal
field theory on surfaces with quark loops as boundaries. Recent results on
self-avoiding random surfaces allow to fix almost uniquely such a conformal
theory. As a consequence, some universal relationships among the string tension
, the thickness of the colour flux tube, the deconfinement temperature and a
lower bound of the glueball mass spectrum are found. The general agreement with
the data extracted from recent lattice simulations with different gauge groups
is rather impressive.(Talk held by F.Gliozzi at Lattice'92 , Amsterdam)


title:
Regularity Properties and Pathologies of Position-Space
  Renormalization-Group Transformations

abstract:
  We reconsider the conceptual foundations of the renormalization-group (RG)
formalism, and prove some rigorous theorems on the regularity properties and
possible pathologies of the RG map. Regarding regularity, we show that the RG
map, defined on a suitable space of interactions (= formal Hamiltonians), is
always single-valued and Lipschitz continuous on its domain of definition. This
rules out a recently proposed scenario for the RG description of first-order
phase transitions. On the pathological side, we make rigorous some arguments of
Griffiths, Pearce and Israel, and prove in several cases that the renormalized
measure is not a Gibbs measure for any reasonable interaction. This means that
the RG map is ill-defined, and that the conventional RG description of
first-order phase transitions is not universally valid. For decimation or
Kadanoff transformations applied to the Ising model in dimension $d \ge 3$,
these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| <
\epsilon(\beta) \}$ of the low-temperature part of the first-order
phase-transition surface. For block-averaging transformations applied to the
Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures
for arbitrary magnetic-field strength. Pathologies may also occur in the
critical region for Ising models in dimension $d \ge 4$. We discuss in detail
the distinction between Gibbsian and non-Gibbsian measures, and give a rather
complete catalogue of the known examples. Finally, we discuss the heuristic and
numerical evidence on RG pathologies in the light of our rigorous theorems.


title: The effective potential and the renormalisation group

abstract:
  We discuss renormalisation group improvement of the effective potential both
in general and in the context of $O(N)$ scalar $\p^4$ and the Standard Model.
In the latter case we find that absolute stability of the electroweak vacuum
implies that $m_H\geq 1.95m_t-189~GeV$, for $\as (M_Z) = 0.11$. We point out
that the lower bound on $m_H$ {\it decreases\/} if $\as (M_Z)$ is increased.


title: The $I=1$, $J=1$ channel of the O(4) $\lambda \phi^4_4$ theory

abstract:
  A Monte Carlo simulation of the $O(4)$ $\lambda \phi^4$ theory in the broken
phase is performed on a hypercubic lattice in search of an $I=1$, $J=1$
resonance. We investigate the region of the cutoff theory where the interaction
is strong as it is there that a resonance would be expected to have a better
chance to form. In that region the presence of an $I=1$, $J=1$ resonance with
mass below the cutoff is excluded. NOTE: The full ps file is also available via
anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and
use for username "anonymous" and for password your name. The file is in the
directory pub/vranas (to go to that directory type: cd pub/vranas) and is
called lat92_proc_rho.ps (to get it type: get lat92_proc_rho.ps)


title: A better large $N$ expansion for chiral Yukawa models

abstract:
  We consider the most general renormalizable chiral Yukawa model with
$SU(3)_{\rm color}$ replaced by $SU(N_c)$, $SU(2)_{\rm L}$ replaced by $SU(N_w
)$ and $U(1)_{Y}$ replaced by $U(1)^{N_w -1}$ in the limit $N_c
\rightarrow\infty$, $N_w \rightarrow\infty$ with the ratio
$\rho=\sqrt{{N_w}\over{N_c}} \ne 0,\infty$ held fixed. Since for $N_w \ge 3$
only one renormalizable Yukawa coupling per family exists and there is no
mixing between families the limit is appropriate for the description of the
effects of a heavy top quark when all the other fermions are taken to be
massless. The large $N=\sqrt{N_{c} N_{w}}$ expansion is expected to be no worse
quantitatively in this model that in the purely scalar case and the $N=\infty$
limit is soluble even when the model is regularized non--perturbatively. A
rough estimate of the triviality bound on the Yukawa coupling is equivalent to
$m_t \le 1~TeV$.


title: Meson-Meson Scattering in Lattice QED_2+1

abstract:
  Scattering phase shifts of a meson-meson system in staggered 3-dimensional
lattice QED are computed. The main task of the simulation is to obtain a
discrete set of two-body energy levels. These are extracted from a 4-point time
correlation matrix and then used to obtain scattering phase shifts. The results
for the l=0 and l=2 partial waves are consistent with short- range repulsion
and intermediate-range attraction of the residual meson- meson interaction.


title: The Shape of Inflated Vesicles

abstract:
  The conformation and scaling properties of self-avoiding fluid vesicles with
zero extrinsic bending rigidity subject to an internal pressure increment
$\Delta p>0$ are studied using Monte Carlo methods and scaling arguments. With
increasing pressure, there is a first-order transition from a collapsed
branched polymer phase to an extended inflated phase. The scaling behavior of
the radius of gyration, the asphericities, and several other quantities
characterizing the average shape of a vesicle are studied in detail. In the
inflated phase, continuously variable fractal shapes are found to be controlled
by the scaling variable $x=\Delta p N^{3\nu/2}$ (or equivalently, $y = {<V>}/
N^{3\nu/2}$), where $N$ is the number of monomers in the vesicle and $V$ the
enclosed volume. The scaling behavior in the inflated phase is described by a
new exponent $\nu=0.787\pm 0.02$.


title: Gauge invariant extremization

abstract:
  Recently, Duncan and Mawhinney introduced a method to find saddle points of
the action in simulations of non-abelian lattice gauge theory. The idea, called
`extremization', is to minimize $\int(\delta S/\delta A_\mu)^2$ instead of the
action $S$ itself as in conventional `cooling'. The method was implemented in
an explicitly gauge variant way, however, and gauge dependence showed up in the
results. Here we present a gauge invariant formulaton of extremization on the
lattice, applicable to any gauge group and any lattice action. The procedure is
worked out in detail for U(1) and SU(N) lattice gauge theory with the plaquette
action.


title: Perturbative Corrections for Staggered Fermion Bilinears

abstract:
  We calculate the perturbative corrections to fermion bilinears that are used
in numerical simulations when extracting weak matrix elements using staggered
fermions. This extends previous calculations of Golterman and Smit, and Daniel
and Sheard. In particular, we calculate the corrections for non-local bilinears
defined in Landau gauge with gauge links excluded. We do this for the simplest
operators, i.e. those defined on a $2^4$ hypercube, and for tree level improved
operators which live on $4^4$ hypercubes. We also consider gauge invariant
operators in which the ``tadpole'' contributions are suppressed by projecting
the sums of products of gauge links back in to the gauge group. In all cases,
we find that the variation in the size of the perturbative corrections is
smaller than those with the gauge invariant unimproved operators. This is most
strikingly true for the smeared operators. We investigate the efficacy of the
mean-field method of Lepage and Mackenzie at summing up tadpole contributions.
In a companion paper we apply these results to four-fermion operators.


title: On reflection positive formulation of chiral gauge theories on a lattice

abstract:
  A formulation of chiral gauge theories on a lattice which is both reflection
positive and gauge invariant is discussed.


title: The Interface Tension in Quenched QCD at the Critical Temperature

abstract:
  We present results for the confinement-deconfinement interface tension
$\alpha_{cd}$ of quenched QCD. They were obtained by applying Binder's
histogram method to lattices of size $L^2\times L_z\times L_t$ for $L_t=2$ and
$L=8,10,12\mbox{ and }14$ with $L_z=30$ for $L=8$ and $L_z=3L$ otherwise. The
use of a multicanonical algorithm and cylindrical geometries have turned out to
be crucial for the numerical studies.


title: The Isgur-Wise Limit on the Lattice

abstract:
  We construct the Isgur-Wise limit of QCD in a form appropriate to lattice
gauge theory techniques. The formulation permits a calculation of heavy quark
processes even when the momentum transfers are much larger than the inverse
lattice spacing. Applications include semi-leptonic heavy quark decay and
scattering processes, including the computation of the nonperturbative part of
the Isgur-Wise universal function.


title: Pure-gauge SU(2) on large lattices

abstract:
  We have calculated the $q\bar q$ potential over a wide range of lattice
separations on a $48^3\cdot56$ lattice at $\beta = 2.85$. We are able to
investigate both long-range and (by correcting for the effects of lack of
rotational invariance) short-range potentials. From the former we estimate the
string tension and from the latter we are able to investigate asymptotic
scaling. Fitting to this enables us to give an estimate for the
$\Lambda$-parameter of pure-gauge SU(2).


title: The Running Coupling from SU(3) Potentials

abstract:
  From an accurate determination of the inter-quark potential, one can study
the running coupling constant for a range of $R$-values and hence estimate the
scale $\Lambda_{\overline{\rm MS}}$. Detailed results are presented for $SU(3)$
pure gauge theory from a study of a $36^4$ lattice at $\beta=6.5$. (to appear
in Proceedings of Lattice 1992 - Amsterdam)


title: Hadron Spectroscopy with Dynamical Wilson Fermions at beta=5.3

abstract:
  We present results from simulations of lattice QCD using two flavors of
dynamical Wilson fermions at a lattice coupling $\beta=5.3$ on $16^3 \times 32$
lattices at two hopping parameters, $\kappa=0.1670$ and $0.1675$, leading to
$m_\pi \approx 0.44$ and $0.33$ respectively. We show spectroscopy for S-wave
hadrons and compare our results to other recent simulations with dynamical
Wilson fermions. (Complete postscript file can be obtained by anonymous ftp
from ftp.scri.fsu.edu as file "lat92.ps" from directory "pub/heller".)


title: The Degrees of Freedom in Hot Quenched QCD

abstract:
  In quenched QCD, on lattices with $\nt=4$, the absence of a pole in the
pseudoscalar meson channel for $T>T_c$ is demonstrated. A set of effective
4-fermi couplings is extracted. It is observed that this coupling is small in
the vector channel for all $T>T_c$, but not in the pseudoscalar channel. The
temperature dependence of hadronic parameters below \tc{} is found to be small.
NOTE: Latex source, no figures, needs espcrc2.sty from hep-lat macros.


title: Problems with the Quenched Approximation in the Chiral Limit

abstract:
  In the quenched approximation, loops of the light singlet meson (the $\eta'$)
give rise to a type of chiral logarithm absent in full QCD. These logarithms
are singular in the chiral limit throwing doubt upon the utility of the
quenched approximation. In previous work, I summed a class of diagrams, leading
to non-analytic power dependencies such as $\cond\propto
m_q^{-\delta/(1+\delta)}$. I suggested, however, that these peculiar results
could be redefined away. Here I give an alternative derivation of the results,
based on the renormalization group, and argue that they cannot be redefined
away. I discuss the evidence (or lack thereof) for such effects in numerical
data.


title: A Gauge-fixed Hamiltonian for Lattice QCD

abstract:
  We study the gauge fixing of lattice QCD in 2+1 dimensions, in the
Hamiltonian formulation. The technique easily generalizes to other theories and
dimensions. The Hamiltonian is rewritten in terms of variables which are gauge
invariant except under a single global transformation. This paper extends
previous work, involving only pure gauge theories, to include matter fields.


title: Finite Size Effects on the QCD Spectrum Revisited

abstract:
  We have continued our study of finite size effects in the QCD spectrum on
lattices ranging in size from $8^3\times 24$ to $16^3\times24$. We have
increased our statistics for quark mass $am_q=0.025$ for the smallest lattice
size. In addition, we have studied quark mass 0.0125 for lattice sizes
$12^3\times24$ and $16^3\times24$. These lattice sizes correspond to a box
1.8--3.6 fm on a side when the rho mass at zero quark mass is used to set the
scale. We discuss the nucleon to rho mass ratio at a smaller value of
$m_\pi/m_\rho$ than previously studied with two dynamical flavors.


title:
Multigrid for propagators of staggered fermions in four-dimensional
  $SU(2)$ gauge fields

abstract:
  Multigrid (MG) methods for the computation of propagators of staggered
fermions in non-Abelian gauge fields are discussed. MG could work in principle
in arbitrarily disordered systems. The practical variational MG methods tested
so far with a ``Laplacian choice'' for the restriction operator are not
competitive with the conjugate gradient algorithm on lattices up to $18^4$.
Numerical results are presented for propagators in $SU(2)$ gauge fields.


title:
The confined-deconfined interface tension, wetting, and the spectrum of
  the transfer matrix

abstract:
  The reduced tension $\sigma_{cd}$ of the interface between the confined and
the deconfined phase of $SU(3)$ pure gauge theory is determined from numerical
simulations of the first transfer matrix eigenvalues. At $T_c = 1/L_t$ we find
$\sigma_{cd} = 0.139(4) T_c^2$ for $L_t = 2$. The interfaces show universal
behavior because the deconfined-deconfined interfaces are completely wet by the
confined phase. The critical exponents of complete wetting follow from the
analytic interface solutions of a $\Z(3)$-symmetric $\Phi^4$ model in three
dimensions. We find numerical evidence that the confined-deconfined interface
is rough.


title:
Surface Tension, Surface Stiffness, and Surface Width of the
  3-dimensional Ising Model on a Cubic Lattice

abstract:
  We compute properties of the interface of the 3-dimensional Ising model for a
wide range of temperatures and for interface extensions up to 64 by 64. The
interface tension sigma is obtained by integrating the surface energy density
over the inverse temperature beta. The surface stiffness coefficient kappa is
determined. We also study universal quantities like xi^2 sigma and xi^2 kappa.
The behavior of the interfacial width on lattices up to 512 times 512 times 27
is also investigated.


title: Lattice Charge Overlap and the Elastic Limit

abstract:
  The results of a lattice simulation of time-separated charge overlap for the
charged pion are discussed. The expected result $\sim {\rm exp}[-(E_q -
m_{\pi})t\,]$ for large charge density overlap time separations, $t$, is
clearly visible in the Fourier transform, indicating that the elastic limit can
be achieved at low to medium momentum values on present-sized lattices. The
implications of this result for direct lattice simulations of hadron structure
functions are discussed and a brief presentation of the lattice formalism is
given.


title: Lattice Analysis of Two-Point Hadronic Correlators in the QCD Vacuum

abstract:
  Results from the first lattice QCD analysis of vacuum correlators of local
hadronic currents using dispersion relations are presented. We have explored
the vector, pseudoscalar, axial, and scalar meson channels, and the proton-like
and delta-like baryon channels. The lattice results are shown to agree
qualitatively with experimental results in channels where experimental data
exist, and shed insight into interacting instanton approximations and sum rule
calculations in the other channels.
  3 figures included (as PostScript files): pi.ps, nd.ps, va.ps : Search for
%%% to retrieve the files. Latex file, needs espcrc2.sty (Search for %%%).


title: Random Walks with Long-Range Self-Repulsion on Proper Time

abstract:
  We introduce a model of self-repelling random walks where the short-range
interaction between two elements of the chain decreases as a power of the
difference in proper time. Analytic results on the exponent $\nu$ are obtained.
They are in good agreement with Monte Carlo simulations in two dimensions. A
numerical study of the scaling functions and of the efficiency of the algorithm
is also presented.


title: Observation of FSS for a First Order Phase Transition

abstract:
  We present the results of a multicanonical simulation of the q=20 2-d Potts
model in the transition region. This is a very strong first order phase
transition. We observe, for the first time, the asymptotic finite size scaling
behavior predicted by Borgs and Koteck\'y close to a first order phase
transition point.


title: Three-Loop Results on the Lattice

abstract:
  We present some new three-loop results in lattice gauge theories, for the
Free Energy and for the Topological Susceptibility. These results are an
outcome of a scheme which we are developing (using a symbolic manipulation
language), for the analytic computation of renormalization functions on the
lattice.


title: Fermion induced SU$(N)$ Yang-Mills Theory

abstract:
  We investigate the gauge interaction induced by heavy fermions using both
dimensional and lattice regularization. We study the condition under which
heavy fermions induce a continuum gauge theory.


title: The Quenched Approximation in Health and in Sickness

abstract:
  We present results for physical quantities computed in quenched chiral
perturbation theory and compare them with the corresponding unquenched
expressions. We also point out an apparent theoretical problem of the quenched
approximation. latex, file espcrc2.sty needed (appended at the end: search for
espcrc2.sty).


title: Gribov Copies and Other Gauge Fixing Beasties on the Lattice

abstract:
  Write-up for Lattice'92, held in Amsterdam. preprint LTH 291.
  Comes with 6 PostScript figures and 1 sty-file. We study the nature of gauge
fixing ambiguities in two dimensional gauge theories. We find that these
ambiguities can be related to the asociated spin model. They can be eliminated
by means of a (multigrid) annealing algorithm.


title: Lattice Calculation of Point-to-Point Hadron Current Correlation

abstract:
  Point-to-point correlation functions of hadron currents in the QCD vacuum are
calculated on a lattice and analyzed using dispersion relations, providing
physical information down to small spatial separations. Qualitative agreement
with phenomenological results is obtained in channels for which experimental
data are available, and these correlation functions are shown to be useful in
exploring approximations based on sum rules and interacting instantons.


title: The Gluon Propagator in Momentum Space

abstract:
  We give preliminary numerical results for the gluon propagator evaluated both
in coordinate and momentum space on a 16^3X40 quenched lattice at beta=6.0. Our
findings are compared with earlier results in the literature at zero momentum.
In addition, by considering nonzero momenta we attempt to extract the form of
the propagator and compare it to continuum predictions formulated by Gribov and
others. latex, file espcrc2.sty needed (appended at the end: search for
espcrc2.sty).


title: A streamlined method for chiral fermions on the lattice

abstract:
  We discuss the use of renormalization counterterms to restore the chiral
gauge symmetry in a lattice theory of Wilson fermions. We show that a large
class of counterterms can be implemented automatically by making a simple
modification to the fermion determinant.


title: How Do Fermions Behave on a Random Lattice?

abstract:
  Comparing random lattice, naive and Wilson fermions in two dimensional
abelian background gauge field, we show that the doublers suppressed in the
free field case are revived for random lattices in the continuum limit unless
gauge interactions are implemented in a non--invariant way.


title: Quantum-Gravity Path-Integrals on Simplicial Lattices

abstract:
  Euclidean quantum-gravity path-integrals are investigated within Regge
calculus by computer simulations. The domain of integration is restricted by
introducing a lower limit for the fatness of each simplex. We use the standard
hypercubic triangulation of the 4-torus and irregularly triangulated lattices
obtained by inserting a small number of vertices using barycentric subdivision.
For limited fatness we find an entropy dominated phase with small negative
curvature both for the regular and the irregular triangulation.


title: Strings with Extrinsic Curvature: An Analysis of the Crossover Regime

abstract:
  We present the results of a set of Monte Carlo simulations of Dynamically
Triangulated Random Surfaces embedded in three dimensions with an extrinsic
curvature dependent action. We analyze several observables in the crossover
regime and discuss whether or not our observations are indicative of the
presence of a phase transition.


title: Hamiltonian lattice gauge theory: wavefunctions on large lattices

abstract:
  We discuss an algorithm for the approximate solution of Schrodinger's
equation for lattice gauge theory, using lattice SU(3) as an example. A basis
is generated by repeatedly applying an effective Hamiltonian to a ``starting
state.'' The resulting basis has a cluster decomposition and long-range
correlations. One such basis has about 10^4 states on a 10X10X10 lattice. The
Hamiltonian matrix on the basis is sparse, and the elements can be calculated
rapidly. The lowest eigenstates of the system are readily calculable.


title: Fermion spectrum in the quenched U(1) chiral Wilson-Yukawa model

abstract:
  Nature of charged fermion state is investigated in the quenched U(1) chiral
Wilson-Yukawa model. Fitting the charged fermion propagator with a single
hyperbolic cosine does not yield reliable result. On the other hand the
behaviour of the propagator including large lattice size dependence is well
described by the large Wilson-Yukawa coupling expansion, providing strong
evidence that no charged state exists as an asymptotic particle in this model.


title: Contamination of Excited States in Quenched QCD Hadron Propagators

abstract:
  Quenched QCD hadron spectrum is calculated with Wilson's quark action at
$\beta=5.85$ and 6.0 on a $24^3 \times 54$ lattice. We discuss the problem of
whether we have extracted the mass of the ground state at these $\beta$'s
without contamination of the excited states. We show that the masses of the
first excited states turn out to be consistent with experiment when we are able
to obtain the propagators up to the large time slice region where the
propagators take the asymptotic forms of the ground states.


title: Anomalous Fermion Number Non-Conservation on the Lattice

abstract:
  The anomaly for the fermion number current is calculated on the lattice in a
simple prototype model with an even number of fermion doublets.


title:
Unstable particles in finite volume: The broken phase of the $4$-d
  $O(4)$ non-linear $\sigma$-model

abstract:
  According to a proposal of L\"uscher 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
4-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 $\sg$-particle in our case. We observe the $\sg$-resonance and extract its
mass and its width.


title: A method for putting chiral fermions on the lattice

abstract:
  We describe a method to put chiral gauge theories on the lattice. Our method
makes heavy use of the effective action for chiral fermions in the continuum,
which is in general complex. As an example we discuss the chiral Schwinger
model.