title: The ``Spin'' Structure of the Nucleon - a lattice investigation

abstract:
  We will discuss here an indirect lattice evaluation of the baryon axial
singlet current matrix element. This quantity may be related to the fraction of
nucleon spin carried by the quarks. The appropriate structure function has
recently been measured (EMC experiment). As in this experiment, we find that
the quarks do not appear to carry a large component of the nucleon spin.


title:
Recent developments in chiral gauge theories: Approach of infinitely
  many fermi fields

abstract:
  I present the recent developments in a specific sub-field of chiral gauge
theories on the lattice. This sub-field pertains to the use of infinitely many
fermi fields to describe a single chiral field. In this approach, both
anomalous and anomaly free theories can be discussed in equal footing. It
produces the correct anomaly in the continuum limit. It has the potential to
describe fermion number violating processes in the presence of a gauge field
background with non-trivial topological charge on a finite lattice.


title: Chiral determinant on the lattice -- Anomalies and Instantons

abstract:
  An expression for the lattice effective action induced by chiral fermions in
any even dimensions in terms of an overlap of two states is shown to have
promising properties in two and four dimensions: The correct abelian anomaly is
reproduced and gauge field configurations with non-zero topological charge are
completely suppressed.


title: Fixed Point Actions for Lattice Fermions

abstract:
  The fixed point actions for Wilson and staggered lattice fermions are
determined by iterating renormalization group transformations. In both cases a
line of fixed points is found. Some points have very local fixed point actions.
They can be used to construct perfect lattice actions for asymptotically free
fermionic theories like QCD or the Gross-Neveu model. The local fixed point
actions for Wilson fermions break chiral symmetry, while in the staggered case
the remnant $U(1)_e \otimes U(1)_o$ symmetry is preserved. In addition, for
Wilson fermions a nonlocal fixed point is found that corresponds to free chiral
fermions. The vicinity of this fixed point is studied in the Gross-Neveu model
using perturbation theory.


title: An Exact Local Hybrid Monte Carlo Algorithm for Gauge Theories

abstract:
  We introduce a new Monte Carlo method for pure gauge theories. It is not
intended for use with dynamical fermions. It belongs to the class of Local
Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the
action by updating individual sites or links by following a classical mechanics
trajectory in fictitious time. We choose to update a one-parameter subgroup of
the gauge field on each link of the lattice, and the classical trajectory can
be found in closed form in terms of elliptic functions for this case. We show
that this gives an overrelaxation algorithm with a tunable parameter which,
unlike some previous methods, does not require the numerical integration of the
equations of motion.


title: Fluctuation Induced First Order Phase Transitions

abstract:
  We study a $U(N)\times U(N)$ symmetric scalar field model in four and three
dimensions. First, using our data in four dimensions in the weak coupling
region, we demonstrate explicitly that the observed first order phase
transition is induced by quantum fluctuations. Next, based on the
renormalization group and our new simulation results in three dimensions we
argue that even if the $U_A(1)$ symmetry is restored below the critical
temperature the QCD finite temperature chiral phase transition for two flavor
could be extremely weak first order. Contribution to Lattice '93 proceedings.
Needs espcrc2.sty file (included). Search Figure1.ps, Figure2.ps, ... for
postscript files.


title:
Super-Instantons and the Reliability of Perturbation Theory in
  Non-Abelian Models

abstract:
  In dimension $D\leq 2$ the low temperature behavior of systems enjoying a
continuous symmetry is dominated by super-instantons: classical configurations
of arbitrarily low energy. Perturbation theory in the background of a
super-instanton produces thermodynamic answers for the invariant Green's
functions that differ from the standard ones, but only in non-Abelian models
and only starting at $O(1/\beta^2)$. This effect modifies the $\beta$-function
of the $O(N)$ models and persists in the large $N$ limit of the $O(N)$ models.


title: The pi-N Sigma term - an evaluation using staggered fermions

abstract:
  A lattice calculation of the pi-N sigma term is described using dynamical
staggered fermions. Preliminary results give a sea term comparable in magnitude
to the valence term.


title: Multigrid Monte Carlo in the Sine Gordon model

abstract:
  We pose two questions about the dynamical critical behavior of multigrid
Monte Carlo: Will a multigrid Monte Carlo simulation of the two dimensional
Sine Gordon model exhibit critical slowing down, as expected by a theoretical
analysis of Metropolis acceptance rates? Can we reduce critical slowing down
caused by decreasing acceptance rates on large blocks by performing more
updates on coarser lattices? To this end we simulate the model with a W-cycle
(gamma = 2) and a higher cycle with gamma = 4 using piecewise constant
interpolation. The answer to the first question is positive, the answer to the
second one is negative.


title: Results from a study of the Nambu--Jona-Lasinio model on the lattice

abstract:
  The main results of our analysis of the two flavor Nambu--Jona-Lasinio model
with $SU(2) \times SU(2)$ chiral symmetry on the four--dimensional hypercubic
lattice with naive and Wilson fermions are presented. Large $N$ techniques and
numerical simulations are used to study various properties of the model. The
scalar and pseudoscalar spectrum, the approach to the continuum and chiral
limits, the size of the $1/N$ corrections, and the effects of the zero momentum
fermionic modes on finite lattices are studied. Also, some interesting
observations are made by viewing the model as an embedding theory of the Higgs
sector.


title: On the Meissner effect in SU(2) lattice gauge theory

abstract:
  We investigate the dual superconductor model of color confinement in SU(2)
lattice gauge theory. We find that the transverse distribution of the
longitudinal chromoelectric field between static quarks displays the dual
Meissner effect. We also give evidence that the problem of color confinement
could be approached in the framework of the 't~Hooft's Abelian projection.


title:
Exploring the Dynamics of Three-Dimensional Lattice Gauge Theories by
  External Fields

abstract:
  We investigate the dynamics of three-dimensional lattice gauge theories by
means of an external Abelian magnetic field. For the SU(2) lattice gauge theory
we find evidence of the unstable modes.


title: Fast K System Generators of Pseudorandom Numbers

abstract:
  We suggest fast algorithm for the matrix generator of pseudorandom numbers
based on Kolmogorov-Anosov K systems which has been proposed earlier. This
algorithm reduces $N^{2}$ operation of the matrix generator to $NlnN$ and
essentially reduces the generation time. It also clarifies the algebraic
structure of this type of K system generators.


title: Self-Avoiding Gonihedric Srting and Spin Systems

abstract:
  We classify different theories of self-intersecting random surfaces assigning
special weights to intersections. When self-intersection coupling constant
$\kappa$ tends to zero, then the surface can freely inetrsect and it is
completely self-avoiding when $\kappa$ tends to infinity. Equivalent spin
systems for this general case were constructed. In two-dimension the system
with $\kappa = 0$ is in complete disorder as it is in the case of 2D gauge
Ising system.


title:
Effects of spatial size, lattice doubling and source operator on the
  hadron spectrum with dynamical staggered quarks

abstract:
  We have extended our previous study of the lattice QCD spectrum with 2
flavors of staggered dynamical quarks at $6/g^2=5.6$ and $am_q=0.025$ and 0.01
to larger lattices, with better statistics and with additional sources for the
propagators. The additional sources allowed us to estimate the $\Delta$ mass
and to measure the masses of all mesons whose operators are local in time.
These mesons show good evidence for flavor symmetry restoration, except for the
masses of the Goldstone and non-Goldstone pions. PCAC is observed in that
$m_\pi^2 \propto m_q$, and $f_\pi$ is estimated. Use of undoubled lattices
removes problems with the pion propagator found in our earlier work. Previously
we found a large change in the nucleon mass at a quark mass of $am_q=0.01$ when
we increased the spatial size from 12 to 16. No such effect is observed at the
larger quark mass, $am_q=0.025$. Two kinds of wall source were used, and we
have found difficulties in getting consistent results for the nucleon mass
between the two sources.


title: On the Phase Structure of the Schwinger Model with Wilson Fermions

abstract:
  We study the phase structure of the massive one flavour lattice Schwinger
model on the basis of the finite size scaling behaviour of the partition
function zeroes. At $\beta = 0$ we observe and discuss a possible discrepancy
with results obtained by a different method.


title:
Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising
  Model

abstract:
  The scaling behaviour of the edge of the Lee--Yang zeroes in the four
dimensional Ising model is analyzed. This model is believed to belong to the
same universality class as the $\phi^4_4$ model which plays a central role in
relativistic quantum field theory. While in the thermodynamic limit the scaling
of the Yang--Lee edge is not modified by multiplicative logarithmic
corrections, such corrections are manifest in the corresponding finite--size
formulae. The asymptotic form for the density of zeroes which recovers the
scaling behaviour of the susceptibility and the specific heat in the
thermodynamic limit is found to exhibit logarithmic corrections too. The
density of zeroes for a finite--size system is examined both analytically and
numerically.


title: The First Order Signal in Pure U(1) Gauge Theory May be Fake

abstract:
  We study the deconfinement phase transition of compact $U(1)$ pure lattice
gauge theory with the Wilson action on {\em closed topology} lattices. In
contrast to studies of compact QED on {\em hypercubic lattices with periodic
boundary conditions}, we find no metastability signal at the phase transition
on the lattices with the topology of a sphere. Thus the determination of the
order of this phase transition has to be reconsidered. We argue that different
properties of closed monopole loops on these topological inequivalent lattices
might be responsible for the effect.


title: Wavelets as a variational basis of the XY model

abstract:
  We use Daubechies' orthonormal compact wavelets as a variational basis for
the $XY$ model in two and three dimensions. Assuming that the fluctuations of
the wavelet coefficients are Gaussian and uncorrelated, minimization of the
free energy yields the fluctuation strength of wavelet coefficients at
different scales, from which observables can be computed. This model is able to
describe the low-temperature phase and makes a prediction about the phase
transition temperature.


title: On the top of the energy barrier. Margarita Garcia Perez

abstract:
  We present results related to the search of SU(2) instantons on a geometry
$[0,L]^3\times [0,T]$ obtained using over-improved cooling with fixed boundary
conditions. We also introduce a criterion for finding a sphaleron at the top of
the energy barrier of the instanton path.


title: Running Coupling in SU(3) Yang-Mills Theory

abstract:
  We report about our ongoing computation of running coupling constants in
asymptotically free theories using the recursive finite size scaling technique.
The latest results for the SU(3) Yang-Mills theory are presented.


title: The Improvement Program in Nonrelativistic Lattice QCD

abstract:
  Progress in the improvement program in nonrelativistic lattice QCD is
outlined. The leading radiative corrections to the heavy-quark mass
renormalization, energy shift, and two important kinetic coupling coefficients
are presented. The reliability of tadpole-improved perturbation theory in
determining the energy shift and mass renormalization is demonstrated.


title: Induced Chern-Simons term in lattice QCD at finite temperature

abstract:
  The general conditions for the Chern-Simons action to be induced as a
nonuniversal contribution of fermionic determinant are formulated in the finite
temperature lattice QCD. The dependence of the corresponding action coefficient
on nonuniversal parameters (chemical potentials, vacuum features, etc. ) is
explored. Special attention is paid to the role of $A_0$-condensate if it is
available in this theory.


title:
Critical Slowing Down of Cluster Algorithms for Ising Models Coupled to
  2-d Gravity

abstract:
  We simulate single and multiple Ising models coupled to 2-d gravity using
both the Swendsen-Wang and Wolff algorithms to update the spins. We study the
integrated autocorrelation time and find that there is considerable critical
slowing down, particularly in the magnetization. We argue that this is
primarily due to the local nature of the dynamical triangulation algorithm and
to the generation of a distribution of baby universes which inhibits cluster
growth.


title: Fermion number violation and a two-dimensional Higgs model

abstract:
  The investigation of topological properties of the gauge field in a
two-dimensional Higgs model can help in understanding anomalous fermion number
violation.


title: A Lattice Study of Spin and Flavour Symmetry in Heavy Quark Physics

abstract:
  We present a first test of heavy quark spin-flavour symmetries in matrix
elements for semi-leptonic decays \bar B to D l\bar\nu and \bar B to D^*
l\bar\nu. We show that O(1/m_Q) corrections are small at masses around the
charm for form factors protected by Luke's Theorem, but are of order 30-40 \%
for h_V and h_V/h_{A_{1}}.


title:
A lattice calculation of the branching ratio for $\overline{B}
  \rightarrow K^* \gamma$

abstract:
  Preliminary results are presented on the calculation of the relevant form
factor for the radiative decay $\overline{B} \rightarrow K^* \gamma$ We find
that the form factor is weakly dependent on the spectator quark mass. We
compare the results obtained for a full chiral extrapolation and where this
independence is assumed. Both results are found to be statistically consistent
with the experimental data.


title: Topological Features in a Two-Dimensional Higgs Model

abstract:
  Topological properties of the gauge field in a two-dimensional Higgs model
are investigated. Results of exploratory numerical simulations are presented.


title: Quantum chromodynamics with various number of flavors

abstract:
  The phase structure of QCD with various number of flavors is studied for
Wilson quarks. For the case of $N_F=3$ we find that the finite temperature
deconfining transition is of first order in the chiral limit on an $N_t=4$
lattice. Together with our previous results that the deconfining transition in
the chiral limit is continuous for $N_F=2$ and is first order for $N_F=6$, the
order of the transition is found to be consistent with a prediction of
universality. The case of $SU(2)$ QCD is also studied in the strong coupling
limit and the phase structure is found to be quite similar to the case of
$SU(3)$: There exists a critical number of flavors $N_F^*$ and for $N_F \geq
N_F^*$ the confinement is broken even in the strong coupling limit for light
quarks. $N_F^*=3$ corresponding to 7 for $SU(3)$.


title: The Behavior of Vortex Loops in the 3-d XY Model

abstract:
  The behavior of vortex loops is studied in the 3-d XY model. It is found that
the phase transtiton of the 3-d XY model is caused by percolating vortex loops.


title: Quenched Heavy-Light Decay Constants

abstract:
  We present decay constants from a quenched simulation using both propagating
quarks and the static theory at $\beta=6.2$ on $24^3\times48$. The results
using propagating quarks are used to test scaling laws predicted by the heavy
quark symmetry.


title: New Method for Dynamical Fermions and Chiral-Symmetry Breaking

abstract:
  The reasons for the feasibility of the Microcanonical Fermionic Average
($MFA$) approach to lattice gauge theory with dynamical fermions are discussed.
We then present a new exact algorithm, which is free from systematic errors and
convergent even in the chiral limit.


title: Lattice Computation of a Magnetic Monopole Mass

abstract:
  A single magnetic monopole in pure SU(2) gauge theory is simulated on the
lattice and its mass is computed in the full quantum theory. The results are
relevant for our proposed realization of the dual superconductor hypothesis of
confinement.


title: Computing the Mass of a Magnetic Monopole in SU(2) Gauge Theory


title: Scaling in Steiner Random Surfaces

abstract:
  It has been suggested that the modified Steiner action functional has
desirable properties for a random surface action. In this paper we investigate
the scaling of the string tension and massgap in a variant of this action on
dynamically triangulated random surfaces and compare the results with the
gaussian plus extrinsic curvature actions that have been used previously.


title: Some Interesting Features of Noncompact QED_3

abstract:
  We study the phase diagram of non compact $QED_3$ using the $MFA$ method and
present evidence for a continuous phase transition line at small $N_f$. We also
analyze the chiral structure of the vacuum by means of the computation of the
probability distribution function of the order parameter in the exact chiral
limit.


title: Finite-Size Effect of Hadron Masses with Kogut-Susskind Quarks

abstract:
  We present numerical results and their analyses of finite-size effects of
hadron masses for both quenched and full QCD calculations. We show that they
are much larger for full QCD due to dynamical sea quarks and the associated
breaking of $Z(3)$ symmetry. We also argue that finite-size effects are
non-negligible even for the largest lattice size simulation currently being
made for a very small quark mass. (talk at lattice93)


title: Sea Quark Effects on the Strong Coupling Constant

abstract:
  We present results showing that the strong coupling constant measured in
two-flavor full QCD with dynamical Kogut-Susskind quarks at $\beta=5.7$ exhibit
a 15\% increase due to sea quarks over that for quenched QCD at the scale
$\mu\approx 7$GeV . (talk at lattice93)


title:
High statistics calculations of quenched QCD spectrum using various
  quark sources

abstract:
  We present the results for the hadron spectrum calculated on 400
configurations using point source, wall source and 8-cubic sources, in quenched
QCD with Wilson fermions at $\beta=6.0$ and $K=0.155$ on a $24^3 \times 54$
lattice. The results for the ground state masses obtained with three types of
quark sources agree well with each other. Masses of the first excited states
appear consistent with experimental values within large errors.


title: Topological charge density around static color sources

abstract:
  We analyze the topological structure of quenched QCD in the presence of
static color sources. Distributions of the topological charge density around
static quarks and mesons are computed in both phases of QCD. We observe a
suppression of topological fluctuations in the vicinity of external sources. In
the confinement phase, the suppression occurs in the whole flux tube between
the static quark and antiquark.


title: SU(2) Colour Fields Around Static Sources

abstract:
  First results of an ongoing high statistics study of the colour flux
distribution around static quark sources in SU(2) gauge theory are presented.
The flux tube profiles and widths have been investigated for several quark
separations at beta=2.5 and beta=2.74. The results are tested against Michael's
sum rules.


title: Alpha_s from the Lattice Potential

abstract:
  We present an extensive study on the direct determination of the running
coupling alpha_s from the static quark antiquark force at short distances, in
quenched QCD. We find from our high statistics potential analysis that alpha_qq
exhibits two-loop asymptotic behaviour for momenta as low as .5 GeV. As a
result, we determine the zero flavour Lambda-parameter to be Lambda^0_MSBAR =
0.630(38)\sqrt{\sigma} = 293(18)^{+25}_{-63} MeV. A rough estimate of full QCD
effects leads to the five flavour value alpha_MSBAR(m_Z) = .102^{+6}_{-11}. A
comparison with other lattice results is made.


title: The analysis of Polyakov loop and spin correlators in finite volumes

abstract:
  We derive an analytic expression for point to point correlation functions of
the Polyakov loop based on the transfer matrix formalism. The contributions
from the eigenvalues of the transfer matrix including and beyond the mass gap
are investigated both for the $2d$ Ising model and in finite temperature
$SU(2)$ gauge theory. We find that the leading matrix element shows similar
scaling properties in both models. Just above the critical point we obtain for
$SU(2)$ a Debye screening mass $~\mu_D/T\approx4~$, independent of the volume.
Sorry, figures are not included and can be sent by ordinary mail.


title: QCD correlation functions and instantons

abstract:
  QCD point-to-point correlation functions at distances .2-1 fm are very
different for different channels, and they tell us a lot about inter-quark
interactions. Recent studies based on experimental data, 'instanton liquid'
approach and lattice measurements are reviewed. Agreement between all of them
show that instanton-induced forces dominate the light quark physics, and new
findings by Negele et al, that {\it hadrons survive 'cooling'}, make this
statement obvious. We also argue that {\it chiral symmetery restoration} is due
to breaking of the 'instanton liquid' into {\it polarized} 'instanton
molecules'. % For Lattice-93 proceedings, figures and % hard copies available
at request, sorry.


title: The role of heavy fermions

abstract:
  Heavy dynamical fermions with masses around the cut-off do not change the low
energy physics apart from a finite renormalization of the gauge coupling. In
this paper we study how light the heavy fermions have to be to cause more than
this trivial renormalization.


title: Status of the Higgs Mass Bound

abstract:
  The status of the triviality bound of the Higgs mass in the Minimal Standard
Model is reviewed. It is emphasized that the bound is obtained, in the scalar
sector, by limiting cutoff effects on physical processes. Results from several
regularization schemes, including actions that allow a parameterization and
tuning of the leading cutoff effects, are presented. They lead to the
conclusion that the Minimal Standard Model will describe physics to an accuracy
of a few percent up to energies of the order 2 to 4 times the Higgs mass,
$M_H$, only if $M_H \le 710 \pm 60 ~ GeV$. The status of Higgs and fermion mass
bounds in Higgs-fermion models is also briefly reviewed.


title: Simple Matrix Elements with Dynamical Fermions

abstract:
  We report on studies of simple matrix elements from simulations with two
flavors of sea quarks, both staggered and Wilson. We show the decay constants
of vector and pseudoscalar mesons. The effects of sea quarks are small. These
simulations are done at relatively large lattice spacing compared to most
quenched studies.


title: Evidence for the Role of Instantons in Hadron Structure from Lattice QCD

abstract:
  Cooling is used as a filter on a set of gluon fields sampling the Wilson
action to selectively remove essentially all fluctuations of the gluon field
except for the instantons. The close agreement between quenched lattice QCD
results with cooled and uncooled configurations for vacuum correlation
functions of hadronic currents and for density-density correlation functions in
hadronic bound states provides strong evidence for the dominant role of
instantons in determining light hadron structure and quark propagation in the
QCD vacuum.


title: The (dual) Meissner effect in SU(2) and SU(3) QCD

abstract:
  After making an abelian projection in the maximally abelian gauge, we measure
the distribution of abelian electric flux and monopole currents around an
abelian Wilson loop in $SU(2)$ and $SU(3)$ QCD. The (dual) Meissner effect is
observed clearly. The vacua in the confinement phases of $SU(2)$ and $SU(3)$
are both at around the border between type-1 and type-2 (dual) superconductor.


title:
Phase Diagram of a Lattice $SU(2) \times SU(2)$ Scalar-Fermion Model
  Using the Zaragoza Fermions

abstract:
  We present a calculation of the phase diagram of a $SU(2) \times SU(2)$
chiral Yukawa model with massless decoupled doublers, using a saddle point
approach, both for small and large Yukawa coupling. Some preliminary MonteCarlo
results are also shown.


title:
Scaling Study of the Leptonic Decay Constants of Heavy-Light Mesons: A
  Consumers Report on Improvement Factors

abstract:
  A high statistics calculation, performed at $\beta =5.74,\;6.00$ and $6.26$,
enables us to study the variation of the leptonic decay constants $f_P$ of
heavy pseudoscalar mesons with the lattice spacing $a$. We observe only a weak
$a$ dependence when the standard $\sqrt{2\kappa}$ normalization is used for the
quark fields, whereas application of the Kronfeld-Mackenzie normalization
induces a stronger variation with $a$. Increasing the meson mass from $1.1GeV$
to $2.3GeV$ this situation becomes even more pronounced.


title: Euclidean gravity attracts

abstract:
  We look at gravitational attraction in simplicial gravity using the dynamical
triangulation method. On the dynamical triangulation configurations we measure
quenched propagators of a free massive scalar field. The masses measured from
these propagators show that gravitational attraction is present.


title: Gluon 2- and 3-Point Correlation Functions on the Lattice

abstract:
  I present some preliminary results, obtained in collaboration with C. Bernard
and A. Soni, for the lattice evaluation of 2- and 3-point gluon correlation
functions in momentum space, with emphasis on the amputated 3-gluon vertex
function. The final goal of this approach is the study of the running QCD
coupling constant as defined from the amputated 3-gluon vertex.


title: Chiral gauge theories on the lattice and restoration of gauge symmetry

abstract:
  We investigate a proposal for the construction of models with chiral fermions
on the lattice using staggered fermions. In this approach the gauge invariance
is broken by the coupling of the staggered fermions to the gauge fields. We aim
at a dynamical restoration of the gauge invariance in the full quantum model.
If the gauge symmetry breaking (SB) is not too severe, this procedure could
lead in the continuum limit to the desired gauge invariant chiral gauge theory.


title: Universality of 2d Yukawa and Gross-Neveu models

abstract:
  Evidence for the same universal behavior of 2d Yukawa and Gross-Neveu models
in a certain range of couplings, particularly for $\kappa<0$, is presented.


title:
Non-perturbative investigation of the fermion-Higgs sector of the
  standard model

abstract:
  We present results for the renormalized quartic self-coupling $\lm_R$ and the
renormalized Yukawa coupling $y_R$ in a fermion-Higgs model with two SU(2)
doublets, indicating that with the standard lattice regulator these couplings
cannot become very strong.


title: Chiral gauge theories on the lattice without gauge fixing?

abstract:
  We discuss two proposals for a non-perturbative formulation of chiral gauge
theories on the lattice. In both cases gauge symmetry is broken by the
regularization. We aim at a dynamical restoration of symmetry. If the gauge
symmetry breaking is not too severe this procedure could lead in the continuum
limit to the desired chiral gauge theory.


title: Partially quenched QCD and staggered fermions

abstract:
  We summarize results for partially quenched chiral perturbation theory and
indicate an application to staggered fermion QCD in which the square root of
the determinant is taken to reduce the number of flavors from four to two.


title: Simulations with Complex Measures

abstract:
  Towards a solution to the sign problem in the simulations of systems having
indefinite or complex-valued measures, we propose a new approach which yields
statistical errors smaller than the crude Monte Carlo using absolute values of
the original measures. The 1D complex-coupling Ising model is employed as an
illustration.


title: Monte Carlo Simulations with Indefinite and Complex-Valued Measures

abstract:
  A method is presented to tackle the sign problem in the simulations of
systems having indefinite or complex-valued measures. In general, this new
approach is shown to yield statistical errors smaller than the crude Monte
Carlo using absolute values of the original measures. Exactly solvable,
one-dimensional Ising models with complex temperature and complex activity
illustrate the considerable improvements and the workability of the new method
even when the crude one fails.


title: Tackling the Sign Problem

abstract:
  To tackle the sign problem in the simulations of systems having indefinite or
complex-valued measures, we propose a new approach which yields statistical
errors smaller than the crude Monte Carlo using absolute values of the original
measures. The 1D complex-coupling Ising model is employed as an illustration.


title: An Extraction of Vcb from the Semi-Leptonic B->D* Decay

abstract:
  We present an extraction of Vcb from a lattice calculation of the B->D* decay
matrix elements. We obtain |Vcb| \sqrt{ \frac{ \tauB }{ 1.49 ps } } = 0.037^{+3
\ +5}_{-3 \ -5} from a single parameter fit to the new CLEO data. Email
nmh@uk.ac.ed.ph.th


title: Monte Carlo Simulations of the SU(2) Vacuum Structure

abstract:
  Lattice Monte Carlo simulations are performed for the SU(2) Yang Mills gauge
theory in the presence of an Abelian background with external sources to obtain
information on the effective potential. The goal is to investigate the lowest
Landau mode that, in the continuum one-loop effective potential, is the crucial
mode for instability. It is shown that also in the lattice formulation this
lowest Landau mode plays a very peculiar role, and it is important for the
understanding of the vacuum properties.


title:
On the Correct Convergence of Complex Langevin Simulations for
  Polynomial Actions

abstract:
  There are problems in physics and particularly in field theory which are
defined by complex valued weight functions $e^{-S}$ where $S$ is a polynomial
action $S: R^n \rightarrow C $. The conditions under which a convergent complex
Langevin calculation correctly simulates such integrals are discussed. All
conditions on the process which are used to prove proper convergence are
defined in the stationary limit.


title: Computer Stochastics in Scalar Quantum Field Theory

abstract:
  This is a series of lectures on Monte Carlo results on the non-perturbative,
lattice formulation approach to quantum field theory. Emphasis is put on 4D
scalar quantum field theory. I discuss real space renormalization group, fixed
point properties and logarithmic corrections, partition function zeroes, the
triviality bound on the Higgs mass, finite size effects, Goldstone bosons and
chiral perturbation theory, and the determination of scattering phase shifts
for some scalar models.


title: Chiral gauge theories with domain wall fermions

abstract:
  We have investigated a proposal to construct chiral gauge theories on the
lattice using domain wall fermions. The model contains two opposite chirality
zeromodes, which live on two domain walls. We couple only one of them to a
gauge field, but find that mirror fermions which also couple to the gauge field
always seem to exist.


title: Monopole clusters and critical dynamics in four-dimensional U(1)

abstract:
  We investigate monopoles in four-dimensional compact U(1) with Wilson action.
We focus our attention on monopole clusters as they can be identified
unambiguously contrary to monopole loops. We locate the clusters and determine
their properties near the U(1) phase transition. The Coulomb phase is
characterized by several small clusters, whereas in the confined phase the
small clusters coalesce to one large cluster filling up the whole system. We
find that clusters winding around the periodic lattice are absent within both
phases and during the transition. However, within the confined phase, we
observe periodically closed monopole loops if cooling is applied.


title: QED: Chiral transition and the issue of triviality

abstract:
  I give a review and progress report on studies of lattice QED. I emphasize
analytical results and methods that are applied in data analysis. Also, I
derive some bounds for the critical exponents and establish their connection
with scaling violations. Triviality, as realized in $\phi^4$ theory, is ruled
out on theoretical grounds. I show that the present data, if analyzed
correctly, all lead to the same conclusions. They are compatible with power law
scaling with nongaussian exponents.


title:
Gauge Fixing and Extended Abelian Monopoles in SU(2) Gauge Theory in 2+1
  Dimensions

abstract:
  Extended Abelian monopoles are investigated in SU(2) lattice gauge theory in
three dimensions. Monopoles are computed by Abelian projection in several
gauges, including the maximal Abelian gauge. The number $N_m$ of extended
monopoles in a cube of size $m^3$ (in lattice units) is defined as the number
of elementary ($1^3$) monopoles minus antimonopoles in the cube
($m=1,2,\ldots$). The distribution of $1^3$ monopoles in the nonlocal maximal
Abelian gauge is shown to be essentially random, while nonscaling of the
density of $1^3$ monopoles in some local gauges, which has been previously
observed, is shown to be mainly due to strong short-distance correlations. The
density of extended monopoles in local gauges is studied as a function of
$\beta$ for monopoles of fixed physical ``size'' ($m / \beta = {\rm fixed}$);
the degree of scale violation is found to decrease substantially as the
monopole size is increased. The possibility therefore remains that long
distance properties of monopoles in local gauges may be relevant to continuum
physics, such as confinement.


title: $B_K$ Using Staggered Fermions: An Update

abstract:
  Improved results for $B_K$ are discussed. Scaling corrections are argued to
be of $O(a^2)$, leading to a reduction in the systematic error. For a kaon
composed of degenerate quarks, the quenched result is ${\widehat{B}_K} = 0.825
\pm 0.027 \pm 0.023$.


title:
Portable QCD codes for Massively Parallel Processors. UKQCD
  collaboration

abstract:
  We present a new set of QCD codes in both message passing and data parallel
versions. The message passing package used is PARMACS, although other packages
may be used. Data parallel software is written in High Performance fortran, an
emerging standard based on Fortran 90. Software engineering methods have been
applied to a physics application to create thoroughly tested and documented
codes for the next generation of massively parallel supercomputers.


title:
Sphaleron transition rate in the classical 1+1 dimensional abelian Higgs
  model at finite temperature

abstract:
  We compute the sphaleron transition rate in the 1+1 dimensional abelian Higgs
model at finite temperature, by real time simulation using the classical
canonical ensemble.


title:
Some Non-Perturbative Aspects of Gauge Fixing in Two Dimensional
  Yang-Mills Theory

abstract:
  Gauge fixing in general is incomplete, such that one solves some of the gauge
constraints, quantizes, then imposes any residual gauge symmetries (Gribov
copies) on the wavefunctions. While the Fadeev-Popov determinant keeps track of
the local metric on this gauge fixed surface, the global topology of the
reduced configuration space can be different depending on the treatment of the
residual symmetries, which can in turn affect global properties of the theory
such as the vacuum wavefunction. Pure $SU(N)$ gauge theory in two dimensions
provides a simple yet non-trivial example where the above structure and effects
can be elucidated explicitly, thus displaying physical effects of the treatment
of Gribov copies.


title: A Lattice Calculation of the Heavy Quark Universal Form Factor

abstract:
  A computation of the Isgur-Wise universal form factor using a lattice
implementation of the heavy quark effective theory is described, and the
results of a lattice simulation are presented.


title: Fermion Number Conservation Isn't Fermion Conservation

abstract:
  A nonperturbative regularization of the Standard Model may have a
superficially undesirable exact global U(1) symmetry corresponding to exact
fermion number conservation. We argue that such a formulation can still have
the desired physics of fermion nonconservation, i.e. fermion particle creation
and annihilation by sphaleron transitions. We illustrate our reasoning in
massless axial QED in 1+1 dimensions.


title: Charmonium Spectroscopy From Lattice NRQCD

abstract:
  We present the first set of results for Charmonium Spectroscopy using
Non-Relativistic QCD (NRQCD). For the NRQCD action the leading order
spin-dependent and next to leading order spin-independent interactions have
been included. Clear signals for the s and p hyperfine splittings have been
observed as well as various orbital states.


title: Lattice QCD Calculation of Hadron Scattering Lengths

abstract:
  Method of calculating hadron multi-point functions and disconnected quark
loop contributions which are not readily accessible through conventional
techniques is proposed. Results are reported for pion-pion, pion-nucleon and
nucleon-nucleon scattering lengths and the flavor singlet-non singlet meson
mass splitting estimated in quenched QCD.


title: Strange Quark Physics on the Lattice

abstract:
  We present results for hadrons containing a strange quark in quenched lattice
QCD. We calculate masses and decay constants using 60 gauge configurations with
an O(a)-improved fermion action at beta = 6.2. Using the rho mass to set the
scale, we find hadron masses within two to three standard deviations of
experiment. Direct comparison with experiment for decay constants is obscured
by uncertainty in current renormalisations. Finally, we present preliminary
results on the semi-leptonic decay D->K. We find f_K^+(0)/Z_V = 0.75+5-4 and
f_K^0(0)/Z_V = 0.74+4-4.


title: Critical behaviour of random walks

abstract:
  We have numerically studied the trapping problem in a two-dimensional lattice
where particles are continuously generated. We have introduced interaction
between particles and directionality of their movement. This model presents a
critical behaviour with a rich phase structure similar to spin systems. We
interpret a change in the asymptotic density of particles as a phase
transition. For high directionality the change is abrupt, possibly of first
order. For small directionality the phase transition is of higher order. We
have computed the phase diagram, the volume dependence of the critical point,
and the relaxation time of the system in the large volume limit.


title:
On the existence of a first order phase transition at small vacuum angle
  $\theta$ in the $CP^3$ model

abstract:
  We examine the phase structure of the $CP^3$ model as a function of $\theta$
in the weak coupling regime. It is shown that the model has a first order phase
transition at small $\theta$. We pay special attention to the extrapolation of
the data to the infinite volume. It is found that the critical value of
$\theta$ decreases towards zero as $\beta$ is taken to infinity.


title: Heavy-light physics with NRQCD

abstract:
  First results are obtained for B mesons using a heavy propagator calculated
using NRQCD, and a light Wilson propagator. Results from 13 quenched
configurations of size 16^3 x 48 at \beta = 6.0 give a value for f_{B} of less
than 200 Mev and a B^{*}-B splitting of 32(8) MeV. Superior signal/noise
behaviour is observed over static propagators on the same configurations. No
extrapolation to the b mass for the heavy quark is required.


title: The Isgur-Wise Function

abstract:
  After a brief introduction to the Heavy-Quark Effective Theory (HQET), I
review the extraction of the Isgur-Wise function from lattice QCD calculations
of the matrix elements for semi-leptonic decays of heavy-light pseudoscalar
mesons both into pseudoscalar and into vector mesons. This work is beginning to
test the heavy-quark spin-flavour symmetries around the charm mass and to
indicate the size of $O(1/m_c)$ corrections. An alternative approach to put the
HQET on the lattice offers the prospect of computing the Isgur-Wise function
directly.


title: A review of heavy-heavy spectroscopy

abstract:
  Calculations of the heavy-heavy spectrum present a good opportunity for
precision tests of QCD using lattice techniques. All methods make use of a
non-relativistic expansion of the action and its systematic improvement to
remove lattice artefacts. There was convincing demonstration this year that
these methods work and that the associated perturbation theory is well-behaved.
Comparison to experimental results yields an accurate value for the lattice
spacing, a, a key result in the determination of \alpha_{s}, and (for the first
time this year) the mass of the b quark (4.7(1) GeV).


title: The Finite Temperature Phase Transition in the Lattice SU(2)-Higgs Model

abstract:
  We study the finite temperature transition of SU(2)-Higgs model with lattice
Monte Carlo techniques. We use dimensional reduction to transform the original
4-dimensional SU(2)-gauge + fundamental Higgs theory to an effective
3-dimensional SU(2) + adjoint Higgs + fundamental Higgs model. The simulations
were performed with Higgs masses of 35 and 80 GeV; in both cases we observe a
stronger first order transition than the perturbation theory predicts,
indicating that the dynamics of the transition strongly depend on
non-perturbative effects.


title:
Making chiral fermion actions (almost) gauge invariant using Laplacian
  gauge fixing

abstract:
  Straight foreward lattice descriptions of chiral fermions lead to actions
that break gauge invariance. I describe a method to make such actions gauge
invariant (up to global gauge transformations) with the aid of gauge fixing. To
make this prescription unambiguous, Laplacian gauge fixing is used, which is
free from Gribov ambiguities.


title: Locating analytically critical temperature in some statistical systems

abstract:
  We have found a simple criterion which allows for the straightforward
determination of the order-disorder critical temperatures. The method
reproduces exactly results known for the two dimensional Ising, Potts and
$Z(N<5)$ models. It also works for the Ising model on the triangular lattice.
For systems which are not selfdual our proposition remains an unproven
conjecture. It predicts $\beta_c=0.2656...$ for the two coupled layers of Ising
spins. Critical temperature of the three dimensional Ising model is related to
the free energy of the two layer Ising system.


title:
Systematic study of autocorrelation time in pure SU(3) lattice gauge
  theory

abstract:
  Results of our autocorrelation measurement performed on Fujitsu AP1000 are
reported. We analyze (i) typical autocorrelation time, (ii) optimal mixing
ratio between overrelaxation and pseudo-heatbath and (iii) critical behavior of
autocorrelation time around cross-over region with high statistic in wide range
of $\beta$ for pure SU(3) lattice gauge theory on $8^4$, $16^4$ and $32^4$
lattices. For the mixing ratio K, small value (3-7) looks optimal in the
confined region, and reduces the integrated autocorrelation time by a factor
2-4 compared to the pseudo-heatbath. On the other hand in the deconfined phase,
correlation times are short, and overrelaxation does not seem to matter For a
fixed value of K(=9 in this paper), the dynamical exponent of overrelaxation is
consistent with 2 Autocorrelation measurement of the topological charge on
$32^3 \times 64$ lattice at $\beta$ = 6.0 is also briefly mentioned.


title: Aspects of Dynamical Symmetry Breaking on a Lattice

abstract:
  In the context of four-fermion and gauge interactions, the Schwinger-Dyson
equation for the fermion self-energy function is studied with the Wilson
fermion on a lattice. We find that the critical line obtained by Bardeen, Leung
and Love is modified. No additional Goldstone bosons appear in the spectrum of
fundamental particles. Massive solutions to the Schwinger-Dyson equation turn
out to be possible for a small gauge coupling.


title: Bosonization and the lattice Gross-Neveu model

abstract:
  We consider a lattice version of the bosonized Gross-Neveu model. It is
explicitely chiral symmetric and its numerical simulation does not involve any
anticommuting field. We study its non trivial $1/N$ expansion up to the
next-to-leading term comparing the results with explicit numerical simulations.


title: Hybrid Monte Carlo simulation of polymer chains

abstract:
  We develop the hybrid Monte Carlo method for simulations of single
off-lattice polymer chains. We discuss implementation and choice of simulation
parameters in some detail. The performance of the algorithm is tested on models
for homopolymers with short- or long-range self-repulsion, using chains with
$16\le N\le 512$ monomers. Without excessive fine tuning, we find that the
computational cost grows as $N^{2+z^\prime}$ with $0.64<z^\prime<0.84$. In
addition, we report results for the scaling of the end-to-end distance,
$r_{1N}\sim N^\nu(\ln N)^{-\alpha}$.


title:
A Variational Approach to the Structure and Thermodynamics of Linear
  Polyelectrolytes with Coulomb and Screened Coulomb Interactions

abstract:
  A variational approach is used to calculate free energy and conformational
properties in polyelectrolytes. The true bond and Coulomb potentials are
approximated by a trial isotropic harmonic energy containing monomer-monomer
force constants as variational parameters. By a judicious choice of
representation and the use of incremental matrix inversion, an efficient and
fast-convergent iterative algorithm is constructed, that optimizes the free
energy. The computational demand scales as N^3. The method has the additional
advantage that the entropy is easily computed. An analysis of the high and low
temperature limits is given. Also, the variational formulation is shown to
respect the appropriate virial identities. The accuracy of the approximations
introduced are tested against Monte Carlo simulations for problem sizes ranging
from N=20 to 1024. Very good performance is obtained for chains with unscreened
Coulomb interactions. The addition of salt is described through a screened
Coulomb interaction, for which the accuracy in a certain parameter range turns
out to be inferior to the unscreened case. The reason is that the isotropic
Gaussian Ansatz becomes less efficient with shorter range interactions. As a
by-product a very efficient Monte Carlo algorithm was developed for
comparisons, providing high statistics data for very large sizes - 2048
monomers.


title:
Determination of ${\bf f(\infty)}$ from the Asymptotic Series for ${\bf
  f(x)}$ About ${\bf x=0}$

abstract:
  A difficult and long-standing problem in mathematical physics concerns the
determination of the value of $f(\infty)$ from the asymptotic series for $f(x)$
about $x\!=\!0$. In the past the approach has been to convert the asymptotic
series to a sequence of Pad\'e approximants $\{P^n_n(x)\}$ and then to evaluate
these approximants at $x\!=\!\infty$. Unfortunately, for most physical
applications the sequence $\{P^n_n(\infty)\}$ is slowly converging and does not
usually give very accurate results. In this paper we report the results of
extensive numerical studies for a large class of functions $f(x)$ associated
with strong-coupling lattice approximations. We conjecture that for large $n$,
$P^n_n(\infty)\!\sim\!f(\infty)+B/\ln n $. A numerical fit to this asymptotic
behavior gives an accurate extrapolation to the value of $f(\infty )$.


title:
Hopping Parameter Analysis of Leptonic and Semi-Leptonic Heavy-Light
  Decays

abstract:
  We study leptonic and semi-leptonic decays of D and B mesons. Use of the
Hopping Parameter Expansion (HPE) for two-point functions allows us
continuously to vary the pseudoscalar mass from below m_D up towards m_B. We
compute the pseudoscalar decay constants f_D and f_B, and observe consistency
with the value calculated in the static limit. {}From the measurement of
three-point functions we compute the matrix element relevant to the decay \bar
B -> D l \bar nu_l and extract the Isgur-Wise function xi(v.v'). The HPE
enables us freely to vary the initial state pseudoscalar mass at constant v.v',
and we investigate the 1/m_Q corrections to the heavy-quark limit.


title:
Phase structure and chiral limit of compact lattice QED with Wilson
  fermions

abstract:
  We study the phase structure and chiral limit of $4d$ compact lattice QED
with Wilson fermions (both dynamical and quenched). We use the standard Wilson
action (WA) and also the modified action (MA) with some lattice artifacts
suppressed. We show that lattice artifacts influence the distributions of
eigenvalues $~\lambda_i~$ of the fermionic matrix especially for small values
of $~\lambda_i~$. Our main conclusion is that the chiral limit of compact QED
can be efficiently located using different techniques. Sorry, figures are not
included and can be sent by ordinary mail or Fax.


title: Structure Functions, Form Factors, and Lattice QCD

abstract:
  We present results towards the calculation of the pion electric form factor
and structure function on a $16^3\times 24$ lattice using charge overlap. By
sacrificing Fourier transform information in two directions, it is seen that
the longitudinal four point function can be extracted with reasonable error
bars at low momentum.


title:
Glueball Spectra of SU(2) Gauge Theories in 3 and 4 Dimensions: A
  Comparison with the Isgur-Paton Flux Tube Model

abstract:
  We use the results of recent lattice calculations to obtain (part of) the
mass spectrum of continuum SU(2) gauge theory in both 2+1 and 3+1 dimensions.
We compare these spectra to the predictions of the Isgur-Paton flux tube model
for glueballs. We use this comparison to test the reliability of different
aspects of the model and also to learn which aspects of the lattice
calculations it is important to improve upon.


title: Three-point functions in noncompact lattice QED

abstract:
  We calculate fermion-antifermion-"meson" three-point functions in noncompact
lattice QED with dynamical staggered fermions and use them to extract effective
Yukawa couplings. The results are consistent with the hypothesis that QED is
trivial.


title: Computation of the Heavy-Light Decay Constant with NRQCD

abstract:
  Non-relativistic QCD is applied for a lattice computation of the heavy-light
meson decay constant in quenched approximation at $\beta=6.0$. Clear signals
are obtained for the ground state at large times in the correlators, allowing a
reliable extraction of the decay constant. Estimating the current
renormalization factor by the tadpole improvement procedure, we find $f_{B}=$
164(17) MeV for the $B$ meson with $a^{-1}=$ 2.3 GeV, while an extrapolation to
the static limit yields $f_{B}^{\mbox{static}}=$ 247(26) MeV.


title: Isgur-Wise Function on the Lattice

abstract:
  We review our method and numerical results for calculation of the Isgur-Wise
function on the lattice. We present a discussion of the systematic errors.
Using recent experimental results, we find $V_{cb} = 0.044\pm 0.005\pm .007$.
Contribution to Lattice '93 proceedings. Needs espcrc2.sty file (included after
\end{document}). Search Figure1.ps for postscript files.


title: Minimal U(1) Gauge Fields in Two Dimensions

abstract:
  Gribov copies of the vacuum in two dimensional compact U(1) lattice gauge
models are constructed. On the basis of this a gauge fixing algorithm is
developped, wich finds the minimum of the sum of link field squares. Numerical
experience in a two dimensional Higgs model with fixed length scalar field is
reported and the extension to three and four dimensional U(1) and four
dimensional SU(2) gauge theories is briefly discussed.


title:
Scattering phases in the broken phase of the 4-d O(4) non-linear
  sigma-model

abstract:
  Using Luescher's method we determine the elastic scattering phases in the
broken phase of the 4-dimensional O(4) non-linear sigma-model from the
two-particle energy spectrum in a Monte-Carlo study on finite lattices. In the
isospin-0-channel we observe the sigma-resonance and extract its mass and its
width. In all scattering channels investigated the results are consistent with
perturbative calculations.


title:
How well do lattice simulations reproduce the different aspects of the
  geometric Schwinger model

abstract:
  We compare continuum and lattice formulation of the geometric Schwinger Model
on the torus. The lattice reproduces the $U(1)_A$ anomaly, related to
non-trivial topological gauge configurations and zero modes.


title: Renormalization of Massive Lattice Fermions

abstract:
  The renormalization of a general action for massive lattice fermions is
discussed. The analysis applies for all $m_q a$. Preliminary results for the
self energy at one loop in perturbation theory are presented.


title:
Multicanonical multigrid Monte Carlo method and effective
  autocorellation time

abstract:
  We report tests of the recently proposed multicanonical multigrid Monte Carlo
method for the two-dimensional $\Phi^4$ field theory. Defining an effective
autocorrelation time we obtain real time improvement factors of about one order
of magnitude compared with standard multicanonical simulations.


title: An investigation into a wavelet accelerated gauge fixing algorithm

abstract:
  We introduce an acceleration algorithm for coulomb gauge fixing, using the
compactly supported wavelets introduced by Daubechies. The algorithm is similar
to Fourier acceleration. Our provisional numerical results for $SU(3)$ on
$8^{4}$ lattices show that the acceleration based on the DAUB6 transform can
reduce the number of iterations by a factor up to 3 over the unaccelerated
algorithm. The reduction in iterations for Fourier acceleration is
approximately a factor of 7.


title: Adding Gauge Fields to Kaplan's Fermions

abstract:
  We experiment with adding dynamical gauge field to Kaplan (defect) fermions.
In the case of U(1) gauge theory we use an inhomogenous Higgs mechanism to
restrict the 3d gauge dynamics to a planar 2d defect. In our simulations the 3d
theory produce the correct 2d gauge dynamics. We measure fermion propagators
with dynamical gauge fields. They posses the correct chiral structure. The
fermions at the boundary of the support of the gauge field (waveguide) are
non-chiral, and have a mass two times heavier than the chiral modes. Moreover,
these modes cannot be excited by a source at the defect; implying that they are
dynamically decoupled. We have also checked that the anomaly relation is
fullfilled for the case of a smooth external gauge field. This is an uuencoded
ps-file. Use 'uudecode hepchiral.ps.Z' and 'uncompress hepchiral.ps.Z' to
produce the psfile.


title:
Masses and Decay Constants of Heavy-Light Mesons Using the Multistate
  Smearing Technique

abstract:
  We present results for f_B and masses of low-lying heavy-light mesons.
Calculations were performed in the quenched approximation using multistate
smearing functions generated from a spinless relativistic quark model
Hamiltonian. Beta values range from 5.7 to 6.3, and light quark masses
corresponding to pion masses as low as 300 MeV are computed at each value. We
use the 1P--1S charmonium splitting to set the overall scale.


title: Non-Perturbative Renormalisation of Composite Operators

abstract:
  It is shown that the renormalisation constants of two quark operators can be
accurately determined (to a precision of a few per-cent using 18 gluon
configurations) using Chiral Ward identities. A method for computing
renormalisation constants of generic composite operators without the use of
lattice perturbation theory is proposed.


title:
Specific Heat Exponent for the 3-d Ising Model from a 24-th Order High
  Temperature Series

abstract:
  We compute high temperature expansions of the 3-d Ising model using a
recursive transfer-matrix algorithm and extend the expansion of the free energy
to 24th order. Using ID-Pade and ratio methods, we extract the critical
exponent of the specific heat to be alpha=0.104(4).


title: Analytical calculation of critical temperatures in some spin systems

abstract:
  A new method for locating analytically critical temperatures is discussed. It
is exact for selfdual systems. When applied the two coupled layers of Ising
spins it deviates from our preliminary Monte Carlo estimates by 1.5 standard
deviations. It predicts critical temperature of the three dimensional Ising
model in terms of the solution of the two layer Ising system.


title: QED on a momentum lattice

abstract:
  We investigate the possibility of doing momentum space lattice simulations as
an alternative to the conventional method. The procedure is introduced and
tested for quenched QED2 and quenched QED3. Interesting physical applications
to unquenched QED3 and quenched QED4 are also briefly discussed.


title:
The Leptonic Decay Constants of $\bar{Q}q$ Mesons and the Lattice
  Resolution

abstract:
  We present a high statistics study of the leptonic decay constant $f_P$ of
heavy pseudoscalar mesons using propagating heavy Wilson quarks within the
quenched approximation, on lattices covering sizes from about 0.7~fm to 2~fm.
Varying $\beta$ between 5.74 and 6.26 we observe a sizeable $a$ dependence of
$f_P$ when one uses the quark field normalization that was suggested by
Kronfeld and Mackenzie, compared with the weaker dependence observed for the
standard relativistic norm. The two schemes come into agreement when one
extrapolates to $a \rightarrow 0$. The extrapolations needed to reach the
continuum quantity $f_B$ introduce large errors and lead to the value
$f_B=0.18(5)$~GeV in the quenched approximation. This suggests that much more
effort will be needed to obtain an accurate lattice prediction for $f_B$.


title:
Interface tension in SU(3) lattice gauge theory at finite temperatures
  on an $N_t=2$ lattice

abstract:
  The surface tension $\sigma$ of the confined-deconfined interface is
calculated in pure $SU(3)$ lattice gauge theory at finite temperatures
employing the operator and integral methods on a lattice of a size $8^2\times
N_z\times 2$ with $N_z=16$ and 40. Analyses of non-perturbative corrections in
asymmetry response functions strongly indicate that the use of one-loop values
for the response functions lead to an overestimate of $\sigma$ in the operator
method. The operator method also suffers more from finite-size effects due to a
finite thickness of the interface, leading us to conclude that the integral
method yields more reliable values for $\sigma$. Our result with the integral
method $\sigma/T_c^3=0.134(16)$ is consistent with earlier results and also
with that obtained with a transfer matrix method. Result is also reported on
$\sigma$ obtained on a lattice $18^2\times 48\times 4$ with the integral
method.


title: Two-Point Functions of Four-Dimensional Simplicial Quantum Gravity

abstract:
  We investigate the interaction mechanism of pure quantum gravity in Regge
discretization. We compute volume-volume and link-link correlation functions.
In a preliminary analysis the forces turn out to be of Yukawa type, at least on
our finite lattice being away from the continuum limit.


title: Nonperturbative Studies of Quantum Gravity

abstract:
  We investigate quantum gravity in the path integral formulation using the
Regge calculus. Restricting the quadratic link lengths of the originally
triangular lattice the path integral can be transformed to the partition
function of a spin system with higher couplings on a Kagome lattice. Various
measures acting as external field were considered. Extensions to matter fields
and higher dimensions are discussed.


title: Two-Dimensional Lattice Gravity as a Spin System

abstract:
  Quantum gravity is studied in the path integral formulation applying the
Regge calculus. Restricting the quadratic link lengths of the originally
triangular lattice the path integral can be transformed to the partition
function of a spin system with higher couplings on a Kagome lattice. Various
measures acting as external field are considered. Extensions to matter fields
and higher dimensions are discussed.


title:
On the behaviour of spatial Wilson loops in the high temperature phase
  of Lattice Gauge Theories

abstract:
  The behaviour of the space-like string tension in the high temperature phase
is studied. Data obtained in the $Z_2$ gauge model in (2+1) dimensions are
compared with predictions of a simple model of a fluctuating flux tube with
finite thickness. It is shown that in the high temperature phase contributions
coming from the fluctuations of the flux tube vanish. As a consequence we also
show that in (2+1) dimensional gauge theories the thickness of the flux tube
coincides with the inverse of the deconfinement temperature.


title: The present status of non-compact lattice QED

abstract:
  We give a 1993 update of non-compact lattice QED, in particular the chiral
condensate, finite size effects and meson mass ratios.
  We compare descriptions of the phase transition. Our previous conclusions
remain valid.


title: Baryon-Baryon Potentials on the Lattice

abstract:
  The interaction of spatially extended heavy baryons is investigated in the
framework of lattice QCD with dynamical quarks. It is shown that the expected
dipole forces have a very short range and that the baryon-antibaryon
interaction is more attractive than the baryon-baryon interaction. Sea quarks
play a minor important role.


title: Gluon Versus Meson Exchange in Hadron-Hadron Systems on the Lattice

abstract:
  The interaction of spatially extended heavy hadrons is investigated in the
framework of lattice QCD with dynamical quarks. In addition to the
baryon-baryon potential results for the baryon-antibaryon and for the
meson-meson system are presented. It is shown that the expected dipole forces
have a very short range and that sea quarks play a minor important role.


title:
Hamiltonian SU(N) Lattice Gauge Theories With Exact Vacuum States In 2+1
  Dimensions

abstract:
  We investigate (2+1)-d Hamiltonian lattice gauge theory using a class of
Hamiltonians having exactly known vacuum states. These theories are shown to
have a wide range of possible classical continuum limits which differ from that
of the standard Kogut-Susskind Hamiltonian. This conclusion is at variance with
some previously published results. We examine the quantum continuum behavior of
these theories by both analytic and numerical methods including plaquette space
integration and standard Monte Carlo techniques. String tension and variational
estimates for the $J^{\rm PC}=0^{++}$ glueball spectra are presented for SU(3).
We find that in spite of the wide range of classical behavior predicted, these
theories correspond to only two distinct quantum systems in the weak coupling
limit. One of these quantum limits gives string tensions and glueball states
which show scaling in weak coupling which agrees with the perturbative
prediction for the (2+1)-d problem.


title: Damaging 2D Quantum Gravity

abstract:
  We investigate numerically the behaviour of damage spreading in a Kauffman
cellular automaton with quenched rules on a dynamical $\phi^3$ graph, which is
equivalent to coupling the model to discretized 2D gravity. The model is
interesting from the cellular automaton point of view as it lies midway between
a fully quenched automaton with fixed rules and fixed connectivity and a
(soluble) fully annealed automaton with varying rules and varying connectivity.
In addition, we simulate the automaton on a fixed $\phi^3$ graph coming from a
2D gravity simulation as a means of exploring the graph geometry.


title: Sphaleron-Like Processes in a Realistic Heat Bath

abstract:
  We measure the diffusion rate of Chern-Simons number in the (1+1)-dimensional
Abelian Higgs model interacting with a realistic heat bath for temperatures
between 1/13 and 2/3 times the sphaleron energy. It is found that the measured
rate is close to that predicted by the sphaleron approximation at the lower end
of the temperature range considered but falls at least an order of magnitude
short of the sphaleron estimate at the upper end of that range. We show
numerically that the sphaleron approximation breaks down as soon as the
gauge-invariant two-point function yields correlation length close to the
sphaleron size.


title: Light Quark Physics on Different Lattices

abstract:
  The light quark results from three different simulations are summarized. We
get consistent results, within our statistics, between smeared and non smeared
data. A comparison is performed with similar results from the UKQCD
collaboration. All runs have been performed on two 6.4 GF APE computers
\cite{tubo}.


title: D- and B-Meson Semi-Leptonic Decays

abstract:
  Recent results for semi-leptonic decays of $D$ and $B$ mesons at $\beta=6.4$,
using the Wilson action, and at $\beta=6.0$, using the Clover action, are
reported.


title: Decay Constants of Heavy-Light Mesons

abstract:
  The decay constants of the heavy-light pseudoscalar mesons are studied in a
high statistics run using the Wilson action at $\beta=6.0$ and $\beta=6.2$, and
the clover action at $\beta=6.0$. The systematics of $O(a)$ discretisation
errors are discussed. Our best estimates of the decay constants are: $f_D$ =
218(9) MeV, $f_D/f_{Ds}$ = 1.11(1) and we obtain preliminary values for $f_B$.


title:
From Perturbation Theory to Confinement: How the String Tension is built
  up

abstract:
  We study the spatial volume dependence of electric flux energies for SU(2)
Yang-Mills fields on the torus with twisted boundary conditions. The results
approach smoothly the rotational invariant Confinement regime. The would-be
string tension is very close to the infinite volume result already for volumes
of $(1.2 \ {\rm fm.})^3$. We speculate on the consequences of our result for
the Confinement mechanism.


title: Quenched Chiral Perturbation Theory for Baryons

abstract:
  We develop quenched chiral perturbation theory for baryons using the
graded-symmetry formalism of Bernard and Golterman and calculate non-analytic
contributions to the baryon masses coming from quenched chiral loops. The usual
term proportional to $m_{q}^{3/2}$ is substantially altered due to the
cancellation of diagrams with internal quark loops. In addition, the $\eta'$
``hairpin'' vertex leads to a new correction, proportional to $m_{q}^{1/2}$. We
compare our results to numerical lattice data and use them to estimate the size
of the quenching error in the octet baryon masses.


title: Surface modes and chiral symmetry (Wilson Fermions in a box)

abstract:
  We give a Hamiltonian discussion of surface states in an extra dimension as a
basis for chiral fermions in lattice models. Such modes appear with the Wilson
fermion action when the hopping parameter exceeds a critical value. The
association of such states with the closing and reopening of a band gap was
noted by Shockley in 1939. Poster presented by Michael Creutz at Lattice 93.
Uuencoded compressed postscript file.


title:
A Non-Abelian Variation on the Savvidy Vacuum of the Yang-Mills Gauge
  Theory

abstract:
  As a prelude to a truly non-perturbative evaluation of the effective
potential in terms of lattice QCD, the one loop effective potential for a
non-Abelian gauge configuration is calculated using the background field
method. Through a non-trivial correlation between the space and color
orientations the new background field avoids the possible coordinate
singularity, ${\rm Det}B_i^a=0$, observed recently by Ken Johnson and his
collaborators in their Schr\"{o}dinger functional study of the SU(2) Yang-Mills
theory. In addition, since our ansatz generates a constant color magnetic field
through the commutator terms rather than derivative terms, many of the
technical drawbacks the Savvidy ansatz suffers on a lattice can be avoided. Our
one loop study yields qualitatively the same result as that of Savvidy's.


title: Precision $\Upsilon$ Spectroscopy and Fundamental Parameters From NRQCD

abstract:
  We present results from a high precision NRQCD simulation of the quenched
$\Upsilon$ system at $\beta = 6$. We demonstrate a variety of important lattice
techniques, including the perturbative improvement of actions, tadpole
improvement, and multicorrelated fits for extracting the spectrum of excited
states. We present new determinations of $\alpha_s(M_Z)$ and $M_b$, two
fundamental parameters of the Standard Model.


title: Evidence for the Role of Instantons in Hadron Structure from Lattice QCD

abstract:
  Cooling is used as a filter on a set of gluon fields sampling the Wilson
action to selectively remove essentially all fluctuations of the gluon field
except for the instantons. The close agreement between quenched lattice QCD
results with cooled and uncooled configurations for vacuum correlation
functions of hadronic currents and for density-density correlation functions in
hadronic bound states provides strong evidence for the dominant role of
instantons in determining light hadron structure and quark propagation in the
QCD vacuum.


title: The Method of Recursive Counting: Can One Go Further?

abstract:
  After a short review of the Method of Recursive Counting we introduce a
general algebraic description of recursive lattice building. This provides a
rigorous framework for discussion of method's limitations.


title: Complex wave function, Chiral spin order parameter and Phase Problem

abstract:
  We study the two dimensional Hubbard model by use of the ground state
algorithm in the Monte Carlo simulation. We employ complex wave functions as
trial function in order to have a close look at properties such as chiral spin
order ($\chi$SO) and flux phase. For half filling, a particle-hole
transformation leads to sum rules with respect to the Green's functions for a
certain choice of a set of wave functions. It is then analytically shown that
the sum rules lead to the absence of the $\chi$SO. Upon doping, we are
confronted with the sign problem, which in our case %ch appears as a ``phase
problem" due to the phase of the Monte Carlo weights. The average of the phase
shows an exponential decay as a function of inverse temperature similarly to
that of sign by Loh Jr. et. al. . We compare the numerical results with those
of exact numerical calculations.


title: A Possible Origin of the Wilson Lattice Fermion

abstract:
  Considering relevant and irrelevant high-dimension operators for ordinary and
mirror fermions respectively, we show that the Wilson lattice fermion can
originate from a spontaneous symmetry breaking phenomenon. Ward identities, due
to symmetries at the cutoff, guarantee the cancellation of mirror-fermion
contributions and the infrared limit can be achieved. The Wilson parameter
turns out to be fixed at $r\simeq 0.18$, where the vacuum energy of the system
is minimized.


title: A pot-pourri of results in QCD from large lattice simulations on the CM5

abstract:
  We present a status report on simulations being done on $32^3 \times 64$
lattices at $\beta = 6.0$ using quenched Wilson fermions. Results for the
spectrum, decay constants, the kaon B-parameter $B_K$, and semi-leptonic form
factors are given based on the current statistical sample of 28 configurations.
These ``Grand Challenge'' calculations are being done on the CM5 at Los Alamos
in collaboration with G. Kilcup, S. Sharpe and P. Tamayo. We end with a brief
statement of code performance.


title: A Universal Fractal Structure of 2D Quantum Gravity for c > 1

abstract:
  We investigate the fractal structure of $2d$ quantum gravity coupled to
matter by measuring the distributions of so-called baby universes. We
demonstrate that the method works well as long as $c \leq 1$. For $c >1$ it is
not clear what distribution to expect. However, we observe strikingly similar
distributions for various kinds of matter fields with the same $c$. This
indicate that there might be some range of $c >1$ where the central charge of
the matter fields alone determines the fractal structure of gravity coupled to
matter. The hypothesis that the string susceptibility $\g = 1/3$ is found to be
compatible with the data for $1 < c \leq 4$.


title: Gauge Invariance and Confinement in Noncompact Simulations of SU(2)

abstract:
  Wilson loops have been measured at strong coupling, $\beta=0.5$, on a $12^4$
lattice in a noncompact simulation of pure SU(2) in which random compact gauge
transformations impose a kind of lattice gauge invariance. The Wilson loops
suggest a confining potential.


title: Computing Masses and Surface Tension from Effective Transfer Matrices

abstract:
  We propose an effective transfer-matrix method that allows a measurement of
tunnelling correlation lengths that are orders of magnitude larger than the
lattice extension. Combining this method with a particularly efficient
implementation of the multimagnetical algorithm we were able to determine the
interface tension of the 3D Ising model close to criticality with a relative
error of less than 1 per cent.


title: On the Schroedinger functional in QCD

abstract:
  In a series of publications [\ref{LNWW},\ref{Schroedinger}], L\"uscher et al.
have demonstrated the usefulness of the Schr\"odinger functional in pure SU(2)
and SU(3) gauge theory. In this paper, it is shown how their formalism can be
extended to include fermions. In the framework of Wilson's lattice QCD, we
define the Schr\"odinger functional by making use of the transfer matrix
formalism. Boundary conditions for the fermions arise naturally. We then take
the naive continuum limit of the action and show that no lattice peculiarities
are left over. The corresponding free Dirac operator has a unique self-adjoint
extension with purely discrete spectrum and no zero modes.


title: The Strong Coupling from Quarkonia

abstract:
  The status of determinations of $\al_s$ from quarkonia using lattice QCD is
reviewed. We compare the results with those obtained from perturbative QCD.


title: Quenched Staggered Spectrum at Beta=6.0, 6.2 and 6.4

abstract:
  We give a preliminary report on the hadron spectrum on an ensemble of
quenched lattices at $\beta$ values of 6.0, 6.2 and 6.4, using staggered
fermions and collaborators Rajan Gupta and Steve Sharpe. Because of the
relatively small number of configurations we pay marginally more attention to
the question of statistics than in previous analyses. We are unable to
discredit quenched QCD.


title:
Series studies of the Potts model. II: Bulk series for the square
  lattice

abstract:
  The finite lattice method of series expansion has been used to extend
low-temperature series for the partition function, order parameter and
susceptibility of the $q$-state Potts model to order $z^{56}$ (i.e. $u^{28}$),
$z^{47}$, $z^{43}$, $z^{39}$, $z^{39}$, $z^{39}$, $z^{35}$, $z^{31}$ and
$z^{31}$ for $q = 2$, 3, 4, \dots 9 and 10 respectively. These series are used
to test techniques designed to distinguish first-order transitions from
continuous transitions. New numerical values are also obtained for the
$q$-state Potts model with $q>4$.


title:
Series studies of the Potts model. III: The 3-state model on the simple
  cubic lattice

abstract:
  The finite lattice method of series expansion has been used to extend
low-temperature series for the partition function, order parameter and
susceptibility of the $3$-state Potts model on the simple cubic lattice to
order $z^{43}$ and the high-temperature expansion of the partition function to
order $v^{21}$. We use the numerical data to show that the transition is
first-order, and estimate the latent heat, the discontinuity in the
magnetisation, and a number of other critical parameters.


title:
Spontaneous Breaking of Flavor Symmetry and Parity in the
  Nambu-Jona-Lasinio Model with Wilson Fermions

abstract:
  We study the lattice \njl~model with two flavors of Wilson fermions in the
large $N$ limit, where $N$ is the number of `colors'. For large values of the
four-fermion coupling we find a phase in which both, flavor symmetry and
parity, are spontaneously broken. In accordance with general expectations there
are three massless pions on the phase boundary, but only two of them remain
massless inside the broken phase. This is analogous to earlier results obtained
in lattice QCD, indicating that this behavior is a very general feature of the
Wilson term.


title:
A definition of the running coupling constant in a twisted SU(2) lattice
  gauge theory

abstract:
  We propose a definition of the running coupling constant in a SU(2) lattice
gauge theory with twisted boundary conditions. It is based on the correlation
of Polyakov loops extended in a twisted direction at a distance which is a
fixed fraction of the totale lattice size. We make the perturbative calculation
which connects this definition to standard regularization schemes. We find
Lambda_Twisted-Polyakov/Lambda_MSbar = 1.6136(2).


title: Heavy-light and light-light weak matrix elements on the lattice

abstract:
  I review recent developments in lattice weak matrix element calculations. I
focus on on $f_B$ (both with propagating quarks and in the static limit for the
$b$ quark), semi-leptonic form factors for $D$ meson decay, form factors for $B
\to K^* \gamma$, and $B_K$. [Review presented at Lattice '93]


title: A Magnetic Monopole in Pure SU(2) Gauge Theory

abstract:
  The magnetic monopole in euclidean pure SU(2) gauge theory is investigated
using a background field method on the lattice.
  With Monte Carlo methods we study the mass of the monopole in the full
quantum theory.
  The monopole background under the quantum fluctuations is induced by imposing
fixed monopole boundary conditions on the walls of a finite lattice volume.
  By varying the gauge coupling it is possible to study monopoles with scales
from the hadronic scale up to high energies.
  The results for the monopole mass are consistent with a conjecture we made
previously in a realization of the dual superconductor hypothesis of
confinement.


title:
The Isgur-Wise Function: A Lattice Determination from Pseudoscalar -->
  Pseudoscalar Form Factors

abstract:
  Form factors for pseudoscalar --> pseudoscalar decays of heavy-light mesons
are found in quenched lattice QCD with heavy-quark masses in the range of
approximately 1-2 GeV. The Isgur-Wise function, $\xi(\omega)$, is extracted
from these form factors. Results are in good agreement with $\xi(\omega)$
derived from CLEO measurements for B --> D*.


title: Hadronic coupling constants in lattice QCD

abstract:
  We report on calculations of the hadronic coupling constants $g_{\rho\pi\pi}$
and $g_{nn\pi}$ based on lattice QCD with four flavors of dynamical staggered
fermions. By computing 2--point and 3--point Green's functions we have been
able to determine these coupling constants ab initio from QCD; the results are
compatible with the experimental values.


title: Ising-link Quantum Gravity

abstract:
  We define a simplified version of Regge quantum gravity where the link
lengths can take on only two possible values, both always compatible with the
triangle inequalities. This is therefore equivalent to a model of Ising spins
living on the links of a regular lattice with somewhat complicated, yet local
interactions. The measure corresponds to the natural sum over all 2^links
configurations, and numerical simulations can be efficiently implemented by
means of look-up tables. In three dimensions we find a peak in the ``curvature
susceptibility'' which grows with increasing system size. However, the value of
the corresponding critical exponent as well as the behavior of the curvature at
the transition differ from that found by Hamber and Williams for the Regge
theory with continuously varying link lengths.


title: The Nambu-Jona-Lasinio model with staggered fermions

abstract:
  We investigate the neighbourhood of the chiral phase transition in a lattice
Nambu--Jona-Lasinio model, using both Monte Carlo methods and lattice
Schwinger-Dyson equations.


title: Computing the Slope of the Isgur-Wise Function

abstract:
  We propose a method for evaluating the slope (and higher derivatives) of the
Isgur-Wise function at the zero recoil point using lattice simulations. These
derivatives are required for the extrapolation of the experimental data for
$B\rightarrow D^*l\bar\nu$ decays to the zero recoil point, from which the
$V_{cb}$ element of the CKM-matrix can be determined.


title: A Few Points on Point-to-Point Correlation Functions

abstract:
  The short-time regime of QCD two-point correlation functions is examined
through a QCD-Sum-Rule-inspired continuum model. QCD Sum Rule techniques are
tested and alternate nucleon interpolating fields are discussed. The techniques
presented here may be of practical use in determining heavy-light meson decay
constants.


title: Spherically-Symmetric Random Walks in Noninteger Dimension

abstract:
  A previous paper (hep-lat/9311011) proposed a new kind of random walk on a
spherically-symmetric lattice in arbitrary noninteger dimension $D$. Such a
lattice avoids the problems associated with a hypercubic lattice in noninteger
dimension. This paper examines the nature of spherically-symmetric random walks
in detail. We perform a large-time asymptotic analysis of these random walks
and use the results to determine the Hausdorff dimension of the process. We
obtain exact results in terms of Hurwitz functions (incomplete zeta functions)
for the probability of a walker going from one region of the spherical lattice
to another. Finally, we show that the probability that the paths of $K$
independent random walkers will intersect vanishes in the continuum limit if
$D> {{2K}\over{K-1}}$.


title:
Temperature Dependence of Extended and Fractional SU(3) Monopole
  Currents

abstract:
  We examine in pure SU(3) the dependence of extended monopole current k and
cross-species extended monopole current k^{cross} on temperature t, monopole
size L, and fractional monopole charge 1/q. We find that features of both k and
k^{cross} are sensitive to t for a range of L and q. In particular, the
spatial-temporal asymmetry ratios of both k and k^{cross} are sensitive over a
range of L and q to the SU(3) deconfinement transition. The motivation for
studying cross, extended, and fractional monopoles in SU(3) is given.


title: New Results and Long-standing Questions in Finite Temperature QCD

abstract:
  We review recent results on QCD at finite temperature. In particular we will
discuss the chiral phase transition in two flavour QCD and new results on the
excitation spectrum in the plasma phase of QCD.


title: Chiral Perturbation Theory on the Lattice; Strong Coupling Expansion

abstract:
  We evaluate the coefficients of the effective chiral Lagrangian to $O(p^4)$
in the strong coupling, large-N expansion. In this limit we explicitly perform
the functional integral over fundamental degrees of freedom and obtain the
effective chiral Lagrangian. We perform this calculation on the Body Centered
Hypercubical lattice which preserves Euclidean invariance to order $p^4$. We
further discuss how the coefficients could be obtained numerically, out of the
strong-coupling domain.


title: Lattice QCD and Chiral Lagrangians

abstract:
  After a very brief review of the formalism of lattice gauge theories we show
how one can calculate the parameters of the continuum chiral Lagrangians
proceeding through the derivation of an effective lattice chiral Lagrangian as
an intermediary step. The derivation is done in the strong coupling limit. We
also discuss how the derivation could be carried out in the intermediate
coupling domain by numerical simulation techniques. Based on a lecture given by
C. Rebbi at the 1993 ICTP Summer School in High Energy Physics and Cosmology,
to be published in the proceedings of the School (World Scientific Publishing -
Singapore - 1994.)


title: Topography of the cooled $\cal{O}(3)$ vacuum

abstract:
  We investigate the {\it topography\/} of the \o3 vacuum after various degrees
of under-relaxed cooling, using the na\"{\i}ve action density and geometric and
field theoretical definitions of the topological charge density. The results
are presented graphically. (This is a cutdown version of the full paper which
is available via anonymous ftp to suna.amtp.liv.ac.uk in /pub/pss/. The figures
missing from this version are available from the same site.)


title:
Spectroscopy and Renormalisation Group Flow of a Lattice
  Nambu-Jona-Lasinio Model

abstract:
  We investigate a lattice Nambu--Jona-Lasinio model both by the Monte Carlo
method and Schwinger-Dyson equations. A comparison allows the discussion of
finite size effects and the extrapolation to infinite volume. We pay special
attention to the identification of particles and resonances. This enables us to
discuss renormalisation group flows in the neighbourhood of the critical
coupling where the chiral symmetry breaking phase transition takes place. In no
region of the bare parameter space do we find renormalisability for the model.


title: Variational calculation of heavy-light meson properties

abstract:
  We present a new method for the study of heavy-light mesons in the static
approximation of lattice QCD which is optimally effective in isolating ground
and excited states. With ``MOST'' (Maximal Operator Smearing Technique), the
heavy quark is smeared at all possible positions relative to the light quark,
subject to the constraint of cubic symmetry. With correlation functions
constructed using this set as a variational basis, eigenstates of the transfer
matrix are projected out at very small time separations, where statistical
errors are small. We illustrate the utility of the method with preliminary
results for the meson decay constant $f_{B}^{\rm stat}$, binding energies and
wave functions of the lowest states. The method produces dynamically-improved
interpolating fields which can be used for matrix element calculations.


title:
Deep Inelastic Scattering in Improved Lattice QCD. I. The first moment
  of structure functions

abstract:
  We present the complete 1-loop perturbative computation of the
renormalization constants and mixing coefficients of the operators that measure
the first moment of deep inelastic scattering structure functions, employing
the nearest neighbor improved lattice QCD action. The interest of using this
action in Monte Carlo simulations lies in the fact that all terms which in the
continuum limit are effectively of order $a$ ($a$ being the lattice spacing)
have been proven to be absent from on-shell hadronic lattice matrix elements.
  Because of the complexity of the calculations, we have checked the analytical
expression of all Feynman diagrams using Schoonschip. To this end we have
developed a suitable code designed to automatically carry out all the necessary
lattice algebraic manipulations, starting from the elementary building blocks
of each diagram.
  We have found discrepancies with some of the published numbers, but we are in
agreement with the known results on the energy-momentum tensor.


title:
Lattice Perturbation Theory for $O(N)$-Symmetric $\sigma$-Models with
  General Nearest-Neighbour Action I. Conventional Perturbation Theory

abstract:
  We compute the beta-function and the anomalous dimension of all the
non-derivative operators of the theory up to three-loops for the most general
nearest-neighbour O(N)-invariant action together with some contributions to the
four-loop beta-function. These results are used to compute the first analytic
corrections to various long-distance quantities as the correlation length and
the general spin-$n$ susceptibility. It is found that these corrections are
extremely large for $RP^{N-1}$ models (especially for small values of N), so
that asymptotic scaling can be observed in these models only at very large
values of beta. We also give the first three terms in the asymptotic expansion
of the vector and tensor energies.


title:
A Numerical Study of the Hierarchical Ising Model: High Temperature
  Versus Epsilon Expansion

abstract:
  We study numerically the magnetic susceptibility of the hierarchical model
with Ising spins ($\sigma =\pm 1$) above the critical temperature and for two
values of the epsilon parameter. The integrations are performed exactly, using
recursive methods which exploit the symmetries of the model. Lattices with up
to $2^18$ sites have been used. Surprisingly, the numerical data can be fitted
very well with a simple power law of the form $(1- \beta /\beta _c )^{- \gamma}
$for the {\it whole} temperature range. The numerical values for $\gamma $
agree within a few percent with the values calculated with a high-temperature
expansion but show significant discrepancies with the epsilon-expansion. We
would appreciate comments about these results.


title: Mass Relation Between Top and Bottom Quarks

abstract:
  In the framework of the recently proposed electroweak theory on a Planck
lattice, we are able to solve approximately the lattice Dyson equation for the
fermion self-energy functions, and obtain the ratio between the masses of the
$t-$ and $b-$ quarks in terms of the electroweak coupling constants. The
predicted top mass agrees with recent determinations from electroweak
observables.


title: Multicanonical study of $D=2$ $O(3)$ nonlinear $\sigma$-model

abstract:
  We present a new and exploratory approach to determine the
$\Delta\beta(\beta)$-shift in the $O(3)$ nonlinear $\sigma$-model. The method
is based on a scaling hypothesis for a free energy difference, which is assumed
to be valid in a situation where the mass gap correlation length $\xi$ is of
the order or larger than the linear extent $L$ of the considered square lattice
sizes. The free energy difference arises from the finite volume constraint
effective potential of the theory. While the constraint effective potential is
calculated in numerical simulations employing a variant of the multicanonical
ensemble on medium sized lattices, it is possible to estimate
$\Delta\beta(\beta)$ up to a value of $\beta=2.8$ in the standard
parameterization of the model.


title: A Heavy Higgs Particle in the TeV Mass Range ?

abstract:
  The first simulation results are presented on Higgs mass calculations in the
spontaneously broken phase of the Higgs sector in the minimal Standard Model
with higher derivative regulator. A heavy Higgs particle is found in the TeV
mass range in the presence of a complex conjugate ghost pair at higher
energies. The ghost pair evades easy experimental detection and a
nonperturbative reinterpretation of the triviality Higgs mass bound becomes
necessary.


title: The scalar and tensor glueballs in the valence approximation

abstract:
  We evaluate the infinite volume, continuum limit of $0^{++}$ and $2^{++}$
glueball masses in the valence approximation. We find $m_{0^{++}} = 1740 \pm 71
$~MeV and $m_{2^{++}} = 2359 \pm 128 $~MeV, consistent with the interpretation
of $f_0 ( 1710 )$ as the lightest scalar glueball.


title: QCD Spectroscopy

abstract:
  I review recent work on the calculation of hadron masses, decay constants and
wave functions.


title: Effective Sampling of Random Surfaces by Baby Universe Surgery

abstract:
  We propose a new, very efficient algorithm for sampling of random surfaces in
the Monte Carlo simulations, based on so-called baby universe surgery, i.e.
cutting and pasting of baby universes. It drastically reduces slowing down as
compared to the standard local flip algorithm, thereby allowing simulations of
large random surfaces coupled to matter fields. As an example we investigate
the efficiency of the algorithm for 2d simplicial gravity interacting with a
one-component free scalar field. The radius of gyration is the slowest mode in
the standard local flip/shift algorithm. The use of baby universe surgery
decreases the autocorrelation time by three order of magnitude for a random
surface of $0.5 \cdot 10^5$ triangles, where it is found to be $\tau_{int} =
150 \pm 31$ sweeps.


title: Quenching 2D Quantum Gravity

abstract:
  We simulate the Ising model on a set of fixed random $\phi^3$ graphs, which
corresponds to a {\it quenched} coupling to 2D gravity rather than the annealed
coupling that is usually considered. We investigate the critical exponents in
such a quenched ensemble and compare them with measurements on dynamical
$\phi^3$ graphs, flat lattices and a single fixed $\phi^3$ graph.


title:
Analysis and Development of Stochastic Multigrid Methods in Lattice
  Field Theory

abstract:
  We study the relation between the dynamical critical behavior and the
kinematics of stochastic multigrid algorithms. The scale dependence of
acceptance rates for nonlocal Metropolis updates is analyzed with the help of
an approximation formula. A quantitative study of the kinematics of multigrid
algorithms in several interacting models is performed. We find that for a
critical model with Hamiltonian H(phi) absence of critical slowing down can
only be expected if the expansion of <H(phi+psi)> in terms of the shift psi
contains no relevant term (mass term). The predictions of this rule are
verified in a multigrid Monte Carlo simulation of the Sine Gordon model in two
dimensions. Our analysis can serve as a guideline for the development of new
algorithms: We propose a new multigrid method for nonabelian lattice gauge
theory, the time slice blocking. For SU(2) gauge fields in two dimensions,
critical slowing down is almost completely eliminated by this method, in
accordance with the theoretical prediction. The generalization of the time
slice blocking to SU(2) in four dimensions is investigated analytically and by
numerical simulations. Compared to two dimensions, the local disorder in the
four dimensional gauge field leads to kinematical problems.


title: The heavy quark potential in QCD with 2 flavors of dynamical quarks

abstract:
  We compute the heavy quark potential on configurations generated by the
HEMCGC collaboration with dynamical staggered fermions at $6/g^2 = 5.6$ and
with dynamical Wilson fermions at $6/g^2 = 5.3$. The computations are done on
$16^3 \times 32$ lattices, corresponding to physical sizes of about 1.6 and 2.3
fm, respectively. Up to the distances probed no sign of string breaking is
detectable. We also compute the recently proposed scale $r_0$ defined by $r_0^2
F(r_0) = 1.65$.


title: Phase Structure of Four Dimensional Simplicial Quantum Gravity

abstract:
  We present the results of a high statistics Monte Carlo study of a model for
four dimensional euclidean quantum gravity based on summing over
triangulations. We show evidence for two phases; in one there is a logarithmic
scaling on the mean linear extent with volume, whilst the other exhibits power
law behaviour with exponent 1/2. We are able to extract a finite size scaling
exponent governing the growth of the susceptibility peak


title:
Various Abelian Projections of $SU(2)$ Lattice Gluodynamics and
  Aharonov-Bohm Effect in the Field Theory

abstract:
  We show that in general abelian projection of lattice gluodynamics it is not
only monopoles but also strings are present. Both these topological excitations
may be responsible for the confinement of color. We illustrate our ideas by
some explicit results in the Abelian Higgs model with the Villain action.


title: Level Crossing for Hot Sphalerons

abstract:
  We study the spectrum of the Dirac Hamiltonian in the presence of high
temperature sphaleron-like fluctuations of the electroweak gauge and Higgs
fields, relevant for the conditions prevailing in the early universe. The
fluctuations are created by numerical lattice simulations. It is shown that a
change in Chern-Simons number by one unit is accompanied by eigenvalues
crossing zero and a change of sign of the generalized chirality $\tGf=
(-1)^{2T+1} \gf$ which labels these modes. This provides further evidence that
the sphaleron-like configurations observed in lattice simulations may be viewed
as representing continuum configurations.


title:
Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the
  Green's Function

abstract:
  Analytical and numerical methods are applied to principal chiral models on a
two-dimensional lattice and their predictions are tested and compared. New
techniques for the strong coupling expansion of SU(N) models are developed and
applied to the evaluation of the two-point correlation function. The
momentum-space lattice propagator is constructed with precision O(\beta^{10})
and an evaluation of the correlation length is obtained for several different
definitions. Three-loop weak coupling contributions to the internal energy and
to the lattice $\beta$ and $\gamma$ functions are evaluated for all N, and the
effect of adopting the ``energy'' definition of temperature is computed with
the same precision. Renormalization-group improved predictions for the
two-point Green's function in the weak coupling ( continuum ) regime are
obtained and successfully compared with Monte Carlo data. We find that strong
coupling is predictive up to a point where asymptotic scaling in the energy
scheme is observed. Continuum physics is insensitive to the effects of the
large N phase transition occurring in the lattice model. Universality in N is
already well established for $N \ge 10$ and the large N physics is well
described by a ``hadronization'' picture.


title: Computers for Lattice Field Theories

abstract:
  Parallel computers dedicated to lattice field theories are reviewed with
emphasis on the three recent projects, the Teraflops project in the US, the
CP-PACS project in Japan and the 0.5-Teraflops project in the US. Some new
commercial parallel computers are also discussed. Recent development of
semiconductor technologies is briefly surveyed in relation to possible
approaches toward Teraflops computers.


title: Recent Results in Scalar QED

abstract:
  In this talk we present some recent and new results on the phase structure
and the continuum limit of lattice formulation of pure gauge QED coupled to
Higgs fields. We show the presence of second order phase transition lines
allowing for a continuum limit. Nevertheless, finite size analysis shows that
this theory is logarithmically trivial. The role of magnetic monopoles is also
shown.