title: Smeared propagators for lattice hadron spectroscopy

abstract:
  We propose to replace ordinary propagators in lattice operator correlations
entering the determination of hadron masses with space-time smeared
propagators. These are defined as the inverse of the quadratic operator in the
fermion action times its hermitian conjugate. We obtain a cleaner determination
of hadron masses, comparable to the effect of using smeared operators.


title: DEPENDENCE OF THE CURRENT RENORMALISATION CONSTANTS ON THE QUARK MASS

abstract:
  We study the behaviour of the vector and axial current renormalisation
constants $Z_V$ and $Z_A$ as a function of the quark mass, $m_q$. We show that
sizeable $O(am_q)$ and $O(g_0^2 a m_q)$ systematic effects are present in the
Wilson and Clover cases respectively. We find that the prescription of
Kronfeld, Lepage and Mackenzie for correcting these artefacts is not always
successful.


title: RESULTS FOR THE B-MESON DECAY CONSTANT FROM THE APE COLLABORATION

abstract:
  The decay constant for the B-meson in the static limit is calculated using
the Wilson and clover actions at various lattice spacings. We show that both
the contamination of our results by excited states and the effects finite
lattice spacing are at most the order of the statistical uncertainties. A
comparison is made of our results and those obtained in other studies. Values
for $f^{stat}_{B_S}/f^{stat}_B$ and $M_{B_S} - M_B$ are also given.


title: Peeping into the SU(2) Gauge Vacuum

abstract:
  We study thermalised configurations of SU(2) gauge fields by cooling. An
analysis of the effect of cooling is presented and global and statistical
information is extracted.


title: Lattice Charge Overlap I: Elastic Limit of Pi and Rho Mesons

abstract:
  Using lattice QCD on a $16^{3}\times 24$ lattice at $\beta=6.0$, we examine
the elastic limit of charge overlap functions in the quenched approximation for
the pion and rho meson; results are compared to previous direct current
insertion calculations. A good signal is seen for the pion, but the electric
and magnetic rho meson results are considerably noisier. We find that the pion
and rho results are characterized by a monopole mass to rho mass ratio of
$0.97(8)$ and $0.73(10)$, respectively. Assuming the functional form of the
electric and magnetic form factors are the same, we also find a rho meson
g-factor of $g=2.25(34)$, consistent with the nonrelativistic quark model.


title: Some Analytical Results in (2+1) dimensional L.G.T.

abstract:
  We show that, within the framework of suitably chosen approximate effective
actions it is possible to evaluate analytically the string tension, the
spacelike string tension and the deconfinement temperature of (2+1) dimensional
lattice gauge theories. In the case of SU(2) gauge theory our results agree
with those obtained through Montecarlo simulations.


title:
Coordinate space methods for the evaluation of Feynman diagrams in
  lattice field theory

abstract:
  We describe an efficient position space technique to calculate lattice
Feynman integrals in infinite volume. The method applies to diagrams with
massless propagators. For illustration a set of two-loop integrals is worked
out explicitly. An important ingredient is an observation of Vohwinkel that the
free lattice propagator can be evaluated recursively and is expressible as a
linear function of its values near the origin.


title:
Nontrivial Fixed Point in the 4D $\Phi^4$ Lattice Model with Internal
  $O(N)$ Symmetry

abstract:
  It is shown that the infinite dimensional critical surface of general
euclidean lattice actions in a generic four-dimensional scalar field theory
with $\Phi^4$ interactions has a domain of special multicritical points where
higher dimensional operators play a special role. Renormalized trajectories of
higher derivative continuum field theories with nontrivial interactions are
traced back to special ultraviolet stable fixed points on the manifold of
multicritical points. These fixed points have an infinite number of relevant
directions which identify the universality classes of critical higher
derivative field theories. The relevance of the new fixed point structure is
discussed within the context of the triviality Higgs mass bound.


title:
Comment on `Asymptotic Scaling in the Two-Dimensional O(3) sigma-Model
  at Correlation Length 10^5' by S. Caracciolo et al

abstract:
  We explain why in our view an extrapolation from small lattices containing
only perturbative information cannot be sufficient to determine nonperturbative
qunatities and therefore cannot lead to a trustworthy determination of the
correlation length.


title: Deconfining Chiral Transition in QCD on the Lattice

abstract:
  The deconfining chiral transition in finite-temperature QCD is studied on the
lattice using Wilson quarks. After discussing the nature of chiral limit with
Wilson quarks, we first study the case of two degenerate quarks $N_F=2$, and
find that the transition is smooth in the chiral limit on both $N_t=4$ and 6
lattices. For $N_F=3$, on the other hand, clear two state signals are observed
for $m_q \simm{<} 140$ MeV on $\nt=4$ lattices. For a more realistic case of
$N_F=2+1$, i.e.\ two degenerate u and d-quarks and a heavier s-quark, we study
the cases $m_s \simeq 150$ and 400 MeV with $m_u = m_d \simeq 0$: In contrast
to a previous result with staggered quarks, clear two state signals are
observed for both cases, suggesting a first order QCD phase transition in the
real world.


title: Two Loop Computation of a Running Coupling in Lattice Yang-Mills Theory

abstract:
  We compute the two loop coefficient in the relation between the lattice bare
coupling and the running coupling defined through the Schroedinger functional
for the case of pure SU(2) gauge theory. This result is needed as one
computational component to relate the latter to the MSbar-coupling, and it
allows us to implement O(a) improvement of the Schroedinger functional to
two-loop order. In addition, the two-loop beta-function is verified in a
perturbative computation on the lattice, and the behavior of an improved bare
coupling is investigated beyond one loop.


title:
Renormalization of the effective theory for heavy quarks at small
  velocity

abstract:
  The slope of the Isgur-Wise function at the normalization point,
$\xi^{(1)}(1)$,is one of the basic parameters for the extraction of the $CKM$
matrix element $V_{cb}$ from exclusive semileptonic decay data. A method for
measuring this parameter on the lattice is the effective theory for heavy
quarks at small velocity $v$. This theory is a variant of the heavy quark
effective theory in which the motion of the quark is treated as a perturbation.
In this work we study the lattice renormalization of the slow heavy quark
effective theory. We show that the renormalization of $\xi^{(1)}(1)$ is not
affected by ultraviolet power divergences, implying no need of difficult
non-perturbative subtractions. A lattice computation of $\xi^{(1)}(1)$ with
this method is therefore feasible in principle. The one-loop renormalization
constants of the effective theory for slow heavy quarks are computed to order
$v^2$ together with the lattice-continuum renormalization constant of
$\xi^{(1)}(1)$ . We demonstrate that the expansion in the heavy-quark velocity
reproduces correctly the infrared structure of the original (non-expanded)
theory to every order. We compute also the one-loop renormalization constants
of the slow heavy quark effective theory to higher orders in $v^2$ and the
lattice-continuum renormalization constants of the higher derivatives of the
$\xi$ function. Unfortunately, the renormalization constants of the higher
derivatives are affected by ultraviolet power divergences, implying the
necessity of numerical non-perturbative subtractions. The lattice computation
of higher derivatives of the Isgur-Wise function seems therefore problematic.


title:
Form Factors for B -> pi l nu-bar_l and B -> K* gamma Decays on the
  Lattice

abstract:
  We present a unified method for analysing form factors in B -> pi l nu-bar_l
and B -> K* gamma decays. The analysis provides consistency checks on the q^2
and 1/M extrapolations necessary to obtain the physical decay rates. For the
first time the q^2 dependence of the form factors is obtained at the B scale.
In the B -> pi l nu-bar_l case, we show that pole fits to f^+ may not be
consistent with the q^2 behaviour of f^0, leading to a possible factor of two
uncertainty in the decay rate and hence in the value of |V_{ub}|^2 deduced from
it. For B -> K* gamma, from the combined analysis of form factors T_1 and T_2,
we find the hadronisation ratio R_{K^*} of the exclusive B -> K* gamma to the
inclusive b -> s gamma rates is of order 35% or 15% for constant and pole-type
behaviour of T_2 respectively.


title: Demons and Abelian Projection QCD: Action and Crossover

abstract:
  I evaluate S_{APQCD}, the exact action of Abelian projection QCD, using the
microcanonical demon method. Starting with a trial action consisting of L=1,
L=2, & L=3 LxL plaquettes plus a Smit-van-der-Sijs magnetic monopole ``mass''
operator, I show that coefficients of the L=2 and L=3 plaquettes vanish at all
beta_{SU2}. In fact, at strong coupling S_{APQCD} is essentially the 1x1
compact QED action with beta_{U1}=beta_{SU2}/2. Beyond beta_{SU2}>=2, S_{APQCD}
gains an exogenous negative 1x1x1 magnetic monopole mass shift. Note that my
approach differs fundamentally from the Smit-van-der-Sijs approach in that I do
not make an a priori assumption about monopole or plaquette size in S_{APQCD}.
Indeed, these results suggest that QCD monopoles are pointlike, in contrast to
the ``effective'' condensation picture put forth by Smit and van der Sijs.


title: Two-point functions in 4D dynamical triangulation

abstract:
  In the dynamical triangulation model of 4D euclidean quantum gravity we
measure two-point functions of the scalar curvature as a function of the
geodesic distance. To get the correlations it turns out that we need to
subtract a squared one-point function which, although this seems paradoxical,
depends on the distance. At the transition and in the elongated phase we
observe a power law behaviour, while in the crumpled phase we cannot find a
simple function to describe it.


title:
Complex-Temperature Properties of the Ising Model on 2D Heteropolygonal
  Lattices

abstract:
  Using exact results, we determine the complex-temperature phase diagrams of
the 2D Ising model on three regular heteropolygonal lattices, $(3 \cdot 6 \cdot
3 \cdot 6)$ (kagom\'{e}), $(3 \cdot 12^2)$, and $(4 \cdot 8^2)$ (bathroom
tile), where the notation denotes the regular $n$-sided polygons adjacent to
each vertex. We also work out the exact complex-temperature singularities of
the spontaneous magnetisation. A comparison with the properties on the square,
triangular, and hexagonal lattices is given. In particular, we find the first
case where, even for isotropic spin-spin exchange couplings, the nontrivial
non-analyticities of the free energy of the Ising model lie in a
two-dimensional, rather than one-dimensional, algebraic variety in the
$z=e^{-2K}$ plane.


title: On ferrimagnetic phases in chiral Yukawa models

abstract:
  We discuss the phase structure of chiral Yukawa models in the mean-field
approximation. In particular, we examine under which conditions a ferrimagnetic
phase appears, by calculating the slopes of possible second order phase
transition lines near a critical point. Our results contrast with some
statements which appeared in the literature recently.


title: Chiral Symmetry Breaking in Abelian-Projected SU(2) Lattice Gauge Theory

abstract:
  Chiral symmetry breaking parameters are calculated in quenched SU(2) gauge
theory and with Abelian gauge fields projected in maximal Abelian gauge and in
field strength gauge. Maximal Abelian gauge projected fields lead to chiral
condensate values which are quite similar to those of the full nonabelian
theory. Pseudoscalar and vector meson correlators are calculated and found to
be reproduced by the use of maximal Abelian gauge fields for small quark
masses. In field-strength gauge, Abelian-projected fields give a chiral
condensate which closely resembles the results of strongly coupled ($\beta<1$)
gauge theory: the chiral condensate is insensitive to $\beta$ and quark mass
and hence violates scaling badly.


title: The Critical Exponents of Crystalline Random Surfaces

abstract:
  We report on a high statistics numerical study of the crystalline random
surface model with extrinsic curvature on lattices of up to $64^2$ points. The
critical exponents at the crumpling transition are determined by a number of
methods all of which are shown to agree within estimated errors. The
correlation length exponent is found to be $\nu=0.71(5)$ from the
tangent-tangent correlation function whereas we find $\nu=0.73(6)$ by assuming
finite size scaling of the specific heat peak and hyperscaling. These results
imply a specific heat exponent $\alpha=0.58(10)$; this is a good fit to the
specific heat on a $64^2$ lattice with a $\chi^2$ per degree of freedom of 1.7
although the best direct fit to the specific heat data yields a much lower
value of $\alpha$. Our measurements of the normal-normal correlation functions
suggest that the model in the crumpled phase is described by an effective field
theory which deviates from a free field theory only by super-renormalizable
interactions.


title: TUNING TO $N=2$ SUPERSYMMETRY IN THE SU(2) ADJOINT HIGGS-YUKAWA MODEL

abstract:
  The $N=2$ supersymmetric continuum limit is investigated in the SU(2) adjoint
Higgs-Yukawa model using lattice perturbation theory. In the one-loop
renormalization group equations a non-trivial infrared fixed point of coupling
ratios is found. The phase structure at weak couplings is determined by a
numerical study of the one-loop effective potential.


title:
The Phase Transition to the Quark Gluon Plasma: Recent Results from
  Lattice Calculations

abstract:
  We will discuss here some of the recent results obtained from lattice
simulations of QCD at non-zero temperature. Such calculations aim at a
quantitative understanding of the thermodynamics of strongly interacting matter
in equilibrium. We concentrate on a discussion of the equation of state, the
chiral transition in two-flavour QCD and hadronic properties related to chiral
symmetry restoration in the vicinity of $T_c$.


title: DECONFINEMENT AND HOT HADRONS IN CRAYS AND QUADRICS

abstract:
  The equation of state of pure QCD, obtained from lattice QCD, is discussed
for temperatures ranging from $0.9\tc$ to $4\tc$, as well as results on
screening masses, the chiral condensate, and the pion decay constant close to
the deconfinement phase transition in the confined phase of QCD. The equation
of state differs significantly from that of a free gas. There is little
evidence of a temperature dependence in the chiral condensate or the meson
properties, but perhaps some for the nucleon screening mass. Above the phase
transition one sees non-perturbative effects, even though hadron correlators
show the existence of deconfined quarks.


title: Effective meson-meson interaction in 2+1 dimensional lattice QED

abstract:
  A definition of an effective meson-meson interaction adapted to the framework
of a lattice simulation is presented. Results, based on a truncated
momentum-space 4-point time correlation matrix, and preliminary data from a
complementary coordinate-space simulation, are shown.


title: A simulation of the Schwinger model in the overlap formalism

abstract:
  In the continuum, the single flavor massless Schwinger model has an exact
global axial $U(1)$ symmetry in the sector of perturbative gauge fields. This
symmetry is explicitly broken by gauge fields with nonzero topological charge
inducing a nonzero expectation value for the bilinear $\bar\psi\psi$. We show
that a lattice formulation of this model, using the overlap formalism to treat
the massless fermions, explicitly exhibits this phenomenon. A Monte Carlo
simulation of the complete system yields the correct value of the fermion
condensate and shows unambiguously that it originates from the sector of
topological charge equal to unity.


title: THE ELECTROWEAK PHASE TRANSITION ON THE LATTICE

abstract:
  The finite temperature electroweak phase transition is studied on the
lattice. The results of the simulations obtained by the 3-dimensional effective
theories and the 4-dimensional SU(2)-Higgs model are reviewed.


title:
Disappearance of the Abrikosov vortex above the deconfining phase
  transition in SU(2) lattice gauge theory

abstract:
  We calculate the solenoidal magnetic monopole current and electric flux
distributions at finite temperature in the presence of a static quark antiquark
pair. The simulation was performed using SU(2) lattice gauge theory in the
maximal Abelian gauge. We find that the monopole current and electric flux
distributions are quite different below and above the finite temperature
deconfining phase transition point and agree with predictions of the
Ginzburg-Landau effective theory.


title: Phase diagram of d=4 Ising Model with two couplings

abstract:
  We study the phase diagram of the four dimensional Ising model with first and
second neighbour couplings, specially in the antiferromagnetic region, by using
Mean Field and Monte Carlo methods. From the later, all the transition lines
seem to be first order except that between ferromagnetic and disordered phases
in a region including the first-neighbour Ising transition point.


title:
ADJOINT "QUARK" COLOR FIELDS IN FOUR-DIMENSIONAL LATTICE GAUGE THEORY:
  VACUUM SCREENING AND PENETRATION

abstract:
  The fields generated by ``quarks'' in the adjoint representation of SU(2)
color are analyzed in the scaling region of the four-dimensional lattice
theory. Evidence of vacuum screening of adjoint quarks is obtained from a
comparison of quark-antiquark ($Q \bar Q$) flux-tubes for quarks in the adjoint
(``isospin'' $j=1$) and fundamental ($j=1/2$) representations. The component
${\cal E}_j$ of the color-electric field strength in the direction parallel to
the $Q \bar Q$ axis is calculated. Near the quarks the ratio of fields ${\cal
E}_{j=1} / {\cal E}_{j=1/2}$ approaches the value 8/3, which is equal to the
ratio of SU(2) Casimirs. In between the quarks, the ratio falls well below 8/3
at large $R$. ${\cal E}_j$ also falls off rapidly as a function of distance
$x_\perp$ perpendicular to the $Q \bar Q$ axis. However, the ratio ${\cal
E}_{j=1} / {\cal E}_{j=1/2}$ depends very weakly on $x_\perp$. The flux-tubes
in the two representations thus appear to have very similar cross-sections.
This result could imply that the QCD vacuum is dual to a type I superconductor.


title: Cooling and the SU(2) Instanton Vaccuum

abstract:
  We present results of an investigation into the nature of instantons in
4-dimensional pure gauge lattice $SU(2)$\ obtained from configurations which
have been cooled using an under-relaxed cooling algorithm. We discuss ways of
calibrating the cooling and the effects of different degrees of cooling, and
compare our data for the shapes, sizes and locations of instantons with
continuum results. In this paper we extend the ideas and techniques developed
by us for use in $O(3)$, and compare the results with those obtained by other
groups.


title: Multicanonical Recursions

abstract:
  The problem of calculating multicanonical parameters recursively is
discussed. I describe in detail a computational implementation which has worked
reasonably well in practice.


title:
A lattice study of the exclusive $B \to K^* \gamma$ decay amplitude,
  using the Clover action at $\beta=6.0$

abstract:
  We present the results of a numerical calculation of the $B\to K^* \gamma$
form factors. The results have been obtained by studying the relevant
correlation functions at $\beta=6.0$, on an $18^3 \times 64$ lattice, using the
${\rm O(a)}$-improved fermion action, in the quenched approximation. From the
study of the matrix element $<K^*| \bar s \sigma_{\mu\nu} b | B>$ we have
obtained the form factor $T_1(0)$ which controls the exclusive decay rate. The
results are compared with the recent results from CLEO. We also discuss the
compatibility between the scaling laws predicted by the Heavy Quark Effective
Theory (HQET) and pole dominance, by studying the mass- and $q^2$-dependence of
the form factors. From our analysis, it appears that the form factors follow a
mass behaviour compatible with the predictions of the HQET and that the
$q^2$-dependence of $T_2$ is weaker than would be predicted by pole dominance.


title: Phase transition and dynamical-parameter method in U(1) gauge theory

abstract:
  Monte Carlo simulations of the 4-dimensional compact U(1) lattice gauge
theory in the neighborhood of the transition point are made difficult by the
suppression of tunneling between the phases, which becomes very strong as soon
as the volume of the lattice grows to any appreciable size. This problem can be
avoided by making the monopole coupling a dynamical variable. In this manner
one can circumvent the tunneling barrier by effectively riding on top of the
peaks in the energy distribution which meet for sufficiently large monopole
coupling. Here we present an efficient method for determining the parameters
needed for this procedure, which can thus be implemented at low computational
cost also on large lattices. This is particularly important for a reliable
determination of the transition point. We demonstrate the working of our method
on a 16^4 lattice. We obtain an equidistribution of configurations across the
phase transition even for such a relatively large lattice size.


title: A Perturbative Construction of Lattice Chiral Fermions

abstract:
  We perform a renormalization group transformation to construct a lattice
theory of chiral fermions. The field variables of the continuum theory are
averaged over hypercubes to define lattice fields. Integrating out the
continuum variables in perturbation theory we derive a chirally invariant
effective action for the lattice fields. This is consistent with the
Nielsen-Niniomiya theorem because the effective action is nonlocal. We also
construct the axial current on the lattice and we show that the axial anomaly
of the continuum theory is reproduced in the Schwinger model. This shows that
chiral fermions can be regularized on the lattice.


title: On the entropy bound of three dimensional simplicial gravity

abstract:
  It is proven that the partition function of 3-dimensional simplicial gravity
has an exponential upper bound with the following assumption: any three
dimensional sphere $S^3$ is constructed by repeated identification of
neighboring links and neighboring triangles in the boundary of a simplicial
3-ball. This assumption is weaker than the one proposed by other authors.


title:
Multi-Grid Monte Carlo. IV. One-Dimensional $O(4)$-Symmetric Nonlinear
  $\sigma$-Model

abstract:
  We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC)
algorithm with piecewise-constant interpolation and a W-cycle, applied to the
one-dimensional $O(4)$-symmetric nonlinear $\sigma$-model [= $SU(2)$ principal
chiral model], on lattices from $L=128$ to $L=16384$. Our data for the
integrated autocorrelation time $\tau_{int,{\cal M}^2}$ are well fit by a
logarithmic growth. We have no idea why the critical slowing-down is not
completely eliminated.


title: The 2-dimensional non-linear sigma-model on a random latice

abstract:
  The O(n) non-linear $\sigma$-model is simulated on 2-dimensional regular and
random lattices. We use two different levels of randomness in the construction
of the random lattices and give a detailed explanation of the geometry of such
lattices. In the simulations, we calculate the mass gap for $n=3, 4$ and 8,
analysing the asymptotic scaling of the data and computing the ratio of Lambda
parameters $\Lambda_{\rm random}/\Lambda_{\rm regular}$. These ratios are in
agreement with previous semi-analytical calculations. We also numerically
calculate the topological susceptibility by using the cooling method.


title: Effective Yukawa Couplings in Noncompact Lattice QED

abstract:
  We investigate effective Yukawa couplings of mesons to the elementary
fermions in noncompact lattice QED. The couplings are extracted from suitable
fermion-antifermion-meson three-point functions calculated by Monte Carlo
simulations with dynamical staggered fermions. The scaling behaviour is
compatible with expectations from perturbation theory, thus indicating
triviality of QED. The lines of constant Yukawa coupling are compared to flows
of other quantities. Consistency is seen, at most, for weak coupling.


title: The String Tension in Gauge Theories

abstract:
  A review article on string tension concept and their relevance as
non-perturbative quantity on the study of quark confinement in lattice gauge
theories. A detailed description of a variety of methods to measure the string
tension on the lattice and an indication of the most promising developments is
proposed.


title: Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice

abstract:
  Many low energy hadrons, such as the rho, can be observed as resonances in
scattering experiments. A proposal by L\"uscher enables one to determine
infinite volume elastic scattering phases from the two-particle energy spectrum
measured from finite periodic lattices. In this work, we generalize the
formalism to the case where the total momentum of the particles is non-zero;
i.e. the lattice frame is not the center-of-mass frame of the scattering
particles. There are several advantages to this procedure including making a
wider variety of center of mass energies accessible with a fixed lattice
volume, and making the avoided level crossing in a P-wave decay occur with a
smaller volume. The formalism is tested with a simple lattice model of two
fields with different masses and a 3-point coupling in 3+1 dimensions. We find
remarkable agreement between the rest-frame and non-rest-frame scattering.


title:
Exact relation of lattice and continuum parameters in three-dimensional
  SU(2)+Higgs theories

abstract:
  The essential features of the high-temperature electroweak phase transition
are contained in a three-dimensional super-renormalizable effective field
theory. We calculate the exact counterterms needed for lattice simulations of
the SU(2)-part of this theory. Scalar fields in both fundamental and adjoint
representations are included. The three-dimensional U(1)+Higgs theory is also
discussed.


title:
Dimensional Reduction and Non-perturbative generation of magnetic mass
  in non-abelian gauge theory at finite temperature

abstract:
  A non-perturbative mass of $0.2719 g^2 T$ is generated for the magnetic
sector of the $SU(2)$ gauge theory at high temperature due to the condensation
of Polyakov \cite{Pol} monopole and antimonopole which form a magnetic glue
ball. String tension for the spatial wilson loop is calculated which is of the
same order of magnitude and has same temperature dependence as obtained from
lattice simulation.


title: Hadronic Coupling Constants in Lattice QCD

abstract:
  We calculate the hadronic coupling constants $g_{NN\pi}$ and $g_{\rho\pi\pi}$
in QCD, including dynamical quarks in the framework of staggered fermions in
the lattice approach. For the nucleon--pion coupling we obtain $g_{NN\pi} =
13.8 \pm 5.8$, to be compared with the experimental value $13.13 \pm 0.07$. The
$\rho\pi\pi$ coupling has been analysed for two different sets of operators
with the averaged result $g_{\rho\pi\pi} = 4.2 \pm 1.9$ which is to be compared
with the experimental value $6.06 \pm 0.01$.


title: Monte Carlo simulations of 4d simplicial quantum gravity

abstract:
  Dynamical triangulations of four-dimensional Euclidean quantum gravity give
rise to an interesting, numerically accessible model of quantum gravity. We
give a simple introduction to the model and discuss two particularly important
issues. One is that contrary to recent claims there is strong analytical and
numerical evidence for the existence of an exponential bound that makes the
partition function well-defined. The other is that there may be an ambiguity in
the choice of the measure of the discrete model which could even lead to the
existence of different universality classes.


title: One-loop renormalization of the QCD Schr\"odinger functional

abstract:
  In a previous publication, we have constructed the Schr\"odinger functional
in Wilson's lattice QCD. It was found that the naive continuum limit leads to a
well-defined classical continuum theory. Starting from the latter, a formal
continuum definition of the Schr\"odinger functional is given and its saddle
point expansion is carried out to one-loop order of perturbation theory.
Dimensional regularization and heat kernel techniques are used to determine the
one-loop divergences. These are partly canceled by the usual renormalizations
of the quark mass and the coupling constant in QCD. An additional divergence
can be absorbed in a multiplicative renormalization of the quark boundary
fields. The corresponding boundary counterterm is a local polynomial in the
fields, so that we confirm a general expectation of Symanzik.


title: Background field technique and renormalization in lattice gauge theory

abstract:
  Lattice gauge theory with a background gauge field is shown to be
renormalizable to all orders of perturbation theory. No additional counterterms
are required besides those already needed in the absence of the background
field. The argument closely follows the treatment given earlier for the case of
dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS,
background gauge and shift symmetries of the lattice functional integral.


title: Chiral Fermions Coupled to Lattice Gauge Fields

abstract:
  Lattice fermions have well-known difficulties with chiral symmetry. To evade
them it is possible to couple continuum fermions to lattice gauge fields, by
introducing an interpolation of the latter. Following this line of thinking,
this paper presents two Euclidean formulations of the effective action that
appears after functional integration over fermion fields, one for vector-like
and the other for chiral couplings. With suitable finite-mode regulators both
effective actions can be evaluated in a finite computation. The prescriptions
provided here contain some details not found in previous work marrying
continuum fermions to the lattice via an interpolation. For example, the
counter-terms needed to maintain chiral gauge invariance are explicitly given.
By construction coupling-constant renormalization, anomaly structure, and (in
the chiral gauge theory) fermion nonconserving amplitudes all satisfy one's
expectations from perturbative and semi-classical analyses.


title: Dual superconductivity in the SU(2) pure gauge vacuum: a lattice study

abstract:
  We investigate the dual superconductivity hypothesis in pure SU(2) lattice
gauge theory. We focus on the dual Meissner effect by analyzing the
distribution of the color fields due to a static quark-antiquark pair. We find
evidence of the dual Meissner effect both in the maximally Abelian gauge and
without gauge fixing. We measure the London penetration length. Our results
suggest that the London penetration length is a physical gauge-invariant
quantity. We put out a simple relation between the penetration length and the
square root of the string tension. We find that our extimation is quite close
to the extrapolated continuum limit available in the literature. A remarkable
consequence of our study is that an effective Abelian theory can account for
the long range properties of the SU(2) confining vacuum.


title: Scaling and the Fractal Geometry of Two-Dimensional Quantum Gravity

abstract:
  We examine the scaling of geodesic correlation functions in two-dimensional
gravity and in spin systems coupled to gravity. The numerical data support the
scaling hypothesis and indicate that the quantum geometry develops a
non-perturbative length scale. The existence of this length scale allows us to
extract a Hausdorff dimension. In the case of pure gravity we find d_H approx.
3.8, in support of recent theoretical calculations that d_H = 4. We also
discuss the back-reaction of matter on the geometry.


title: Geometrical Origin of Tricritical Points of various U(1) Lattice Models

abstract:
  We review the dual relationship between various compact U(1) lattice models
and Abelian Higgs models, the latter being the disorder field theories of
line-like topological excitations in the systems. We point out that the
predicted first-order transitions in the Abelian Higgs models (Coleman-Weinberg
mechanism) are, in three dimensions, in contradiction with direct numerical
investigations in the compact U(1) formulation since these yield continuous
transitions in the major part of the phase diagram. In four dimensions, there
are indications from Monte Carlo data for a similar situation. Concentrating on
the strong-coupling expansion in terms of geometrical objects, surfaces or
lines, with certain statistical weights, we present semi-quantitative arguments
explaining the observed cross-over from first-order to continuous transitions
by the balance between the lowest two weights (``2:1 ratio'') of these
geometrical objects.


title: Creutz Ratios From Color-Truncated Lattice Configurations

abstract:
  We investigate whether information about Creutz ratios is encoded,
separately, in each gluon color component of numerically generated lattice
configurations. Working in SU(2) lattice gauge theory in Landau gauge, we set
two of the three gluon color components to zero, and compensate for the loss of
two-thirds of the fluctuation by simply rescaling the remaining component by a
factor of $\sqrt{3}$. Creutz ratios are then computed with this "abelianized"
configuration. We find that the Creutz ratios of loops constructed from
abelianized links converge to the usual Creutz ratios in the scaling regime.


title: A NOVEL LOOK AT THE MICHAEL LATTICE SUM RULES

abstract:
  We reconsider the derivation of the Michael lattice sum rules, which relate
the energy and action stored in a flux tube of a quark-antiquark pair to the
static interquark potential, and show that they require essential corrections.
We then find, using the coupling constant sum rule of Karsch, that the total
Minkowski field energy does not match the interquark potential, if one follows
conventional notions. The implications of this result are discussed.


title: TOPOLOGICAL OBJECTS AND CONFINEMENT ON THE LATTICE

abstract:
  First we discuss various topological objects (monopoles, ``minopoles'' and
``hybrids'') which may be important for the confinement mechanism in various
abelian projections. The second topic is the string between quark and
antiquark. The standard quantum string with the Nambu-Goto action exists only
in D=26. If we start from the field theory, in which the string excitations
exist, and change the variables in the path integral to the string variables,
then the Jacobian appears. This Jacobian generates the correction to the
Nambu-Goto action. For this effective action the conformal anomaly cancels in
D=4. Thus we get the quantum string theory in D=4.


title: The Use of Schoonschip and Form in Perturbative Lattice Calculations

abstract:
  Using the formal languages Schoonschip and Form, we have developed general
codes that are able to carry out all the algebraic manipulations needed to
perform analytic lattice calculations, starting from the elementary building
blocks (propagators and vertices) of each Feynman diagram. The main difficulty
resides in the fact that, although there are many built in instructions to deal
with Dirac gamma-matrices, Schoonschip and Form have been conceived having in
mind a continuum theory, which is invariant with respect to the Lorentz group.
On the lattice, on the contrary, a field theory is only invariant with respect
to the hypercubic group, contained in the (euclidean) Lorentz group and not
every pair of equal indices should be summed over. Being impossible to directly
use the `gammatrics' of Schoonschip and Form as they are, special routines have
been developed to correctly treat gamma matrices on the lattice, while using as
much as possible of the built in Schoonschip and Form commands. We have used
our codes to compute, in 1-loop perturbation theory in lattice QCD, the
renormalization constants and mixing coefficients of the operators that enter
in the determination of the first two moments of deep inelastic scattering
structure functions.


title: ``GLUELUMP'' SPECTRUM AND ADJOINT SOURCE POTENTIAL IN LATTICE QCD$_3$

abstract:
  We calculate the potential between ``quarks'' which are in the adjoint
representation of SU(2) color in the three-dimensional lattice theory. We work
in the scaling region of the theory and at large quark separations $R$. We also
calculate the masses $M_{Qg}$ of color-singlet bound states formed by coupling
an adjoint quark to adjoint glue (``gluelumps''). Good scaling behavior is
found for the masses of both magnetic (angular momentum $J=0$) and electric
($J=1$) gluelumps, and the magnetic gluelump is found to be the lowest-lying
state. It is naively expected that the potential for adjoint quarks should
saturate above a separation $R_{\rm scr}$ where it becomes energetically
favorable to produce a pair of gluelumps. We obtain a good estimate of the
naive screening distance $R_{\rm scr}$. However we find little evidence of
saturation in the potential out to separations $R$ of about twice $R_{\rm
scr}$.


title: Lattice sum rules for the colour fields

abstract:
  We analyse the sum rules describing the action and energy in the colour
fields around glueballs, torelons and static potentials.


title:
Comment on "Superinstantons and the Reliability of Perturbation Theory
  in Non-Abelian Models"

abstract:
  In a recent letter (hep-lat/9311019) A. Patrascioiu and E. Seiler argued that
when taking into account "superinstantons configurations" the perturbative
expansion and the beta-function of the two-dimensional non-linear sigma-model
are modified at two loops order. I point out that: (1) perturbation theory in a
superinstanton background is infra-red singular beyond three loops; (2) the new
infra-red singular terms, which change the two loop terms, come from singular
operators - describing superinstanton insertions - in the OPE; (3) taking into
account these operators, the beta-function is not modified. Therefore the
results of Patrascioiu and Seiler do not contradict perturbation theory.


title: Masses and decay constants of the B-system in Lattice QCD

abstract:
  Heavy-light bound states are studied in Lattice QCD with emphasis on
parameters of the B-system relevant to experiment. Results are obtained on
lattices with lattice spacings from about 0.15 fm to 0.06 fm corresponding to
$\beta=5.74, 6.0$ and 6.26, and covering sizes from about 0.7 fm to 2 fm. From
our results at the infinite quark mass limit and from propagating heavy quarks
with mass of about 1-2.5 GeV we extrapolate to the b-quark mass to obtain the
decay constant of the B-meson as well as the mass of $\Lambda_b$ in the
continuum. The necessary extrapolations introduce rather large errors and lead
to the value $f_B=180(50)$ MeV. We compare with the results from other lattice
groups as well as with predictions coming from sum rules. The phenomenological
consequences of this value of $f_B$, together with new experimental
constraints, are briefly discussed.


title: Chiral Phase Transition in Lattice QCD with Wilson Quarks

abstract:
  The nature of the chiral phase transition in lattice QCD is studied for the
cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice
with the temporal direction extension $N_t=4$. We find that the chiral phase
transition is continuous for the case of 2 flavors, while it is of first order
for 3 and 6 flavors.


title: Many Masses on One Stroke: Economic Computation of Quark Propagators

abstract:
  The computational effort in the calculation of Wilson fermion quark
propagators in Lattice Quantum Chromodynamics can be considerably reduced by
exploiting the Wilson fermion matrix structure in inversion algorithms based on
the non-symmetric Lanczos process. We consider two such methods: QMR (quasi
minimal residual) and BCG (biconjugate gradients). Based on the decomposition
$M/\kappa={\bf 1}/\kappa-D$ of the Wilson mass matrix, using QMR, one can carry
out inversions on a {\em whole} trajectory of masses simultaneously, merely at
the computational expense of a single propagator computation. In other words,
one has to compute the propagator corresponding to the lightest mass only,
while all the heavier masses are given for free, at the price of extra storage.
Moreover, the symmetry $\gamma_5\, M= M^{\dagger}\,\gamma_5$ can be used to cut
the computational effort in QMR and BCG by a factor of two. We show that both
methods then become---in the critical regime of small quark
masses---competitive to BiCGStab and significantly better than the standard MR
method, with optimal relaxation factor, and CG as applied to the normal
equations.


title:
Some approximate analytical methods in the study of the self-avoiding
  loop model with variable bending rigidity and the critical behaviour of the
  strong coupling lattice Schwinger model with Wilson fermions

abstract:
  Some time ago Salmhofer demonstrated the equivalence of the strong coupling
lattice Schwinger model with Wilson fermions to a certain 8-vertex model which
can be understood as a self-avoiding loop model on the square lattice with
bending rigidity $\eta = 1/2$ and monomer weight $z = (2\kappa)^{-2}$. The
present paper applies two approximate analytical methods to the investigation
of critical properties of the self-avoiding loop model with variable bending
rigidity, discusses their validity and makes comparison with known MC results.
One method is based on the independent loop approximation used in the
literature for studying phase transitions in polymers, liquid helium and cosmic
strings. The second method relies on the known exact solution of the
self-avoiding loop model with bending rigidity $\eta = 1/\sqrt{2}$. The present
investigation confirms recent findings that the strong coupling lattice
Schwinger model becomes critical for $\kappa_{cr} \simeq 0.38-0.39$. The phase
transition is of second order and lies in the Ising model universality class.
Finally, the central charge of the strong coupling Schwinger model at
criticality is discussed and predicted to be $c = 1/2$.


title: Is There Quantum Gravity in Two Dimensions?

abstract:
  A hybrid model which allows to interpolate between the (original) Regge
approach and dynamical triangulations is introduced. The gained flexibility in
the measure is exploited to study dynamical triangulation in a fixed geometry.
Our numerical results support KPZ exponents. A critical assessment concerning
the apparent lack of gravitational effects in two dimensions follows.


title: Spin Glasses on Thin Graphs

abstract:
  In a recent paper we found strong evidence from simulations that the
Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed
amean-field spin glass transition. The intrinsic interest of considering such
random graphs is that they give mean field results without long range
interactions or the drawbacks, arising from boundary problems, of the Bethe
lattice. In this paper we reprise the saddle point calculations for the Ising
and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We
use standard results from bifurcation theory that enable us to treat an
arbitrary number of replicas and any quenched bond distribution. We note the
agreement between the ferromagnetic and spin glass transition temperatures thus
calculated and those derived by analogy with the Bethe lattice, or in previous
replica calculations. We then investigate numerically spin glasses with a plus
or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models,
paying particular attention to the independence of the spin glass transition
from the fraction of positive and negative bonds in the Ising case and the
qualitative form of the overlap distribution in all the models. The parallels
with infinite range spin glass models in both the analytical calculations and
simulations are pointed out.


title:
Scaling and topology in the 2-d O(3) $\sigma$-model on the lattice with
  the fixed point action

abstract:
  We study scaling properties and topological aspects of the 2--d O(3)
non--linear $\sigma$--model on the lattice with the parametrized fixed point
action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of
the mass gap confirms the good properties of scaling of the fixed point action.
Concerning the topology, lattice classical solutions are proved to be very
stable under local minimization of the action; this outcome ensures the
reliability of the cooling method for the computation of the topological
susceptibility, which indeed reproduces the results of the field theoretical
approach. Disagreement is instead observed with a different approach in which
the fixed point topological charge operator is used: we argue that the
discrepancy is related to the ultraviolet dominated nature of the model.


title: Zeros of the Partition Function for Higher--Spin 2D Ising Models

abstract:
  We present calculations of the complex-temperature zeros of the partition
functions for 2D Ising models on the square lattice with spin $s=1$, 3/2, and
2. These give insight into complex-temperature phase diagrams of these models
in the thermodynamic limit. Support is adduced for a conjecture that all
divergences of the magnetisation occur at endpoints of arcs of zeros protruding
into the FM phase. We conjecture that there are $4[s^2]-2$ such arcs for $s \ge
1$, where $[x]$ denotes the integral part of $x$.


title: Monopole Condensation in Gauge Theory Vacuum

abstract:
  The condensation of monopoles (dual superconductivity) of QCD vacuum is
reviewed. Direct evidence is produced that the system, in the confined phase,
is a dual superconductor.


title: A Lattice Simulation of the SU(2) Vacuum Structure

abstract:
  In this article we analyze the vacuum structure of pure SU(2) Yang-Mills
using non-perturbative techniques. Monte Carlo simulations are performed for
the lattice gauge theory with external sources to obtain the effective
potential. Evidence from the lattice gauge theory indicating the presence of
the unstable mode in the effective potential is reported.


title:
Perfect 3-Dimensional Lattice Actions for 4-Dimensional Quantum Field
  Theories at Finite Temperature

abstract:
  We propose a two-step procedure to study the order of phase transitions at
finite temperature in electroweak theory and in simplified models thereof. In a
first step a coarse grained free energy is computed by perturbative methods. It
is obtained in the form of a 3-dimensional perfect lattice action by a block
spin transformation. It has finite temperature dependent coefficients. In this
way the UV-problem and the infrared problem is separated in a clean way. In the
second step the effective 3-dimensional lattice theory is treated in a
nonperturbative way, either by the Feynman-Bogoliubov method (solution of a gap
equation), by real space renormalization group methods, or by computer
simulations. In this paper we outline the principles for $\varphi ^4$-theory
and scalar electrodynamics. The Ba{\l}aban-Jaffe block spin transformation for
the gauge field is used. It is known how to extend this transformation to the
nonabelian case, but this will not be discussed here.


title: Adjoint 2D QCD and Pure 3D QCD: A Comparison of Spectra

abstract:
  We briefly review the 1+1-dimensional SU(N) gauge theory minimally coupled to
an adjoint scalar, based upon a dimensional reduction of 2+1-dimensional pure
gauge theory, which approximates the dynamics of the transversely polarized
gluon. The lightest glueball states are investigated non-perturbatively using
light-front quantisation in the large-N limit a la 't Hooft, and the physical
meaning of the results elucidated. Comparison is made with recent lattice Monte
Carlo data for 3-dimensional quenched QCD.


title: Noncompact Lattice Formulation of Gauge Theories

abstract:
  We expand the gauge field in terms of a suitably constructed complete set of
Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave
number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation
of lattice QCD (or QED) can be derived by restricting the expansion only to the
$\,0^{th}$-band ($\,n = 0\,$) functions, which are simple continuum
interpolations of discrete values associated with sites or links on a lattice.
The exact continuum theory can be reached through the inclusion of all $\,n =
0\,$ and $\,n \ne 0\,$ bands, without requiring the lattice size $\,\ell \to
0\,$. This makes it possible, at a nonzero $\,\ell\,$, for the lattice coupling
$\,g_\ell\,$ to act as the renormalized continuum coupling. All physical
results in the continuum are, of course, independent of $\,\ell\,$.


title:
Computation of the relation between the bare lattice coupling and the
  MSbar coupling in SU(N) gauge theories to two loops

abstract:
  The perturbation expansion of the MSbar coupling in the SU(N) gauge theory in
powers of the bare lattice coupling is extended to two-loop order. A discussion
of our results has already been published elsewhere. We here describe the
calculation in some detail. It relies on the background field technique and a
recently introduced coordinate space method to evaluate lattice Feynman
integrals.


title:
Perfect observables for the hierarchical non-linear $O(N)$-invariant
  $\sigma$-model

abstract:
  We compute moving eigenvalues and the eigenvectors of the linear
renormalization group transformation for observables along the renormalized
trajectory of the hierarchical non-linear $O(N)$-invariant $\sigma$-model by
means of perturbation theory in the running coupling constant. Moving
eigenvectors are defined as solutions to a Callan-Symanzik type equation.


title:
Chiral phase transition in a lattice fermion--gauge--scalar model with
  U(1) gauge symmetry

abstract:
  The chiral phase transition induced by a charged scalar field is investigated
numerically in a lattice fermion-gauge-scalar model with U(1) gauge symmetry,
proposed recently as a model for dynamical fermion mass generation. For very
strong gauge coupling the transition is of second order and its scaling
properties are very similar to those of the Nambu--Jona-Lasinio model. However,
in the vicinity of the tricritical point at somewhat weaker coupling, where the
transition changes the order, the scaling behavior is different. Therefore it
is worthwhile to investigate the continuum limit of the model at this point.


title: Colour confinement as dual Meissner effect: $SU(2)$ gauge theory

abstract:
  We demonstrate that confinement in $SU(2)$ gauge theory is produced by dual
superconductivity of the vacuum. We show that for $T < T_c$ (temperature of
deconfining phase transition) the $U(1)$ symmetry related to monopole charge
conservation is spontaneously broken; for $T > T_c$ the symmetry is restored.


title:
Interpolated Lattice Gauge Fields and Chiral Fermions in the Schwinger
  Model

abstract:
  The effective action induced by fermions in the chiral Schwinger model with
charges (3,4,5) is investigated. Pauli-Villars regularization is combined with
momentum cut-off for the evaluation of the fermion determinants on continuum
gauge fields interpolated between lattice points. The convergence and gauge
variance are studied numerically on gauge configurations taken from quenched
updating.


title: The Gluon Propagator at High Temperature

abstract:
  We study the gluon propagator in Landau gauge in the deconfined phase of
$SU(2)$ gauge theory. From the long-distance behaviour of correlation functions
of temporal and spatial components of the gauge fields we extract electric
($m_e$) and magnetic ($m_m$) screening masses. For temperatures larger than
twice $T_c$ we find no additional temperature dependence in $m_e(T)/T$, while
$m_m(T)/T$ drops with increasing temperature. The decrease is consistent with
the expected behaviour, $m_m(T) \sim g^2(T)T$. We find $m_e(T) = 2.484(52)T$
and $m_m(T) = 0.466(15) g^2(T) T$.


title: QCD Phase Transition with Strange Quark in Wilson Formalism for Fermions

abstract:
  The nature of QCD phase transition is studied with massless up and down
quarks and a light strange quark, using the Wilson formalism for quarks on a
lattice with the temporal direction extension $N_t=4$. We find that the phase
transition is first order in the cases of both about 150 MeV and 400 MeV for
the strange quark mass. These results together with those for three degenerate
quarks suggest that QCD phase transition in nature is first order.


title: COMBINING MCRG AND FOURIER ACCELERATED LANGEVIN ALGORITHM

abstract:
  We study the implementation of Monte Carlo renormalization group (MCRG) in
momentum space. This technique is most efficient when used in combination with
a Fourier accelerated Langevin algorithm. As a benchmark we calculate the
critical exponents $\nu$ and $\eta$ in the vicinity of both the gaussian and
the Wilson fixed point in $\lambda \phi^4_3$. The results are very competitive
with alternative analytical methods and require a moderate computational effort
only.


title: Meron-Cluster Simulation of the $\theta$-Vacuum in the 2-d $O(3)$-Model

abstract:
  The 2-d $O(3)$-model with a $\theta$-vacuum term is formulated in terms of
Wolff clusters. Each cluster carries a half-integer topological charge. The
clusters with charge $\pm 1/2$ are identified as merons. At $\theta = \pi$ the
merons are bound in pairs inducing a second order phase transition at which the
mass-gap vanishes. The construction of an improved estimator for the
topological charge distribution makes numerical simulations of the phase
transition feasible. The measured critical exponents agree with those of the $k
= 1$ Wess-Zumino-Novikov-Witten model. Our results are consistent with
Haldane's conjecture for 1-d antiferromagnetic quantum spin chains.


title:
Quenched $B_K$-parameter with the Wilson and Clover actions at $\beta =
  6.0$

abstract:
  We present results for the Kaon $B$ parameter from a sample of $200$
configurations using the Wilson action and $460$ configurations using the
Clover action, on a $18^3 \times 64$ lattice at $\beta=6.0$. A slight
improvement of the chiral behaviour of $B_K$ is observed due to the Clover
action. We have also compared the results for $B_K$ obtained from two different
procedures for the boosting of the coupling constant $g$. We observe a strong
dependence of $B_K$ on the prescription adopted for $g$ in the Wilson case,
contrary to the results of the Clover case which are almost unaffected by the
choice of $g$. Combining some recently obtained non perturbative estimates for
the renormalisation constants with our Clover matrix element, we observe a
significant improvement in the chiral behaviour of $B_K$.


title: Systematic errors of L\"uscher's fermion method and its extensions

abstract:
  We study the systematic errors of L\"uscher's formulation of dynamical Wilson
quarks and some of its variants, in the weak and strong coupling limits, and on
a sample of small configurations at finite $\beta$. We confirm the existence of
an optimal window in the cutoff parameter $\varepsilon$, and the exponential
decrease of the error with the number of boson families. A non-hermitian
variant improves the approximation further and allows for an odd number of
flavors. A simple and economical Metropolis test is proposed, which makes the
algorithm exact.


title:
A Connection Between Complex-Temperature Properties of the 1D and 2D
  Spin $s$ Ising Model

abstract:
  Although the physical properties of the 2D and 1D Ising models are quite
different, we point out an interesting connection between their
complex-temperature phase diagrams. We carry out an exact determination of the
complex-temperature phase diagram for the 1D Ising model for arbitrary spin $s$
and show that in the $u_s=e^{-K/s^2}$ plane (i) it consists of $N_{c,1D}=4s^2$
infinite regions separated by an equal number of boundary curves where the free
energy is non-analytic; (ii) these curves extend from the origin to complex
infinity, and in both limits are oriented along the angles $\theta_n =
(1+2n)\pi/(4s^2)$, for $n=0,..., 4s^2-1$; (iii) of these curves, there are
$N_{c,NE,1D}=N_{c,NW,1D}=[s^2]$ in the first and second (NE and NW) quadrants;
and (iv) there is a boundary curve (line) along the negative real $u_s$ axis if
and only if $s$ is half-integral. We note a close relation between these
results and the number of arcs of zeros protruding into the FM phase in our
recent calculation of partition function zeros for the 2D spin $s$ Ising model.


title: Advanced Linked Cluster Expansion. Scalar Fields at Finite Temperature

abstract:
  Linked cluster expansions provide a useful tool for both analytical and
numerical investigations of lattice field theories. The expansion parameter(s)
being the interaction strength(s) fields at neighboured lattice sites are
coupled, they result into convergent hopping parameter like series for free
energies, correlation functions and in particular susceptibilities. We consider
scalar fields with O(N) symmetric nearest neighbour interactions on hypercubic
lattices with possibly finite extension in some directions, thus including
field theories at finite temperature T. We improve known and develop new
techniques and algorithms to increase the order n the expansions can be
computed to in such a way that detailed information on critical behaviour can
be extracted from the susceptibility series. This concerns both simple moments
as well as higher correlations such as 4- and 6-point functions used to define
renormalized coupling constants. Particular emphasis is done on finite
temperature field theory. In order to be able to measure finite T critical
behaviour, the order of explicit computation n has to be sufficiently large
compared to 1/T in lattice units. 2- and 4-point susc. series are computed up
to and including the 18th order and beyond.


title:
FINITE TEMPERATURE PHASE TRANSITION IN QCD WITH STRANGE QUARK: STUDY
  WITH WILSON FERMIONS ON THE LATTICE

abstract:
  The effect of the strange quark in the finite temperature phase transition of
QCD is studied on the lattice. Using the one-plaquette gauge action and the
Wilson quark action, the transition in the chiral limit is shown to be
continuous for the case of degenerate two flavors, $N_F=2$, while it is of
first order for $N_F \geq 3$. For a more realistic case of massless up and down
quarks and a light strange quark, $N_F=2+1$, clear two state signals are
observed both for $m_s \simeq 150$ and 400 MeV. In contrast to a previous
result with staggered quarks, this suggests a first order transition in the
real world. In order to see the implication of these results to the continuum
limit, we started to study these issues using improved actions. First results
using a RG improved gauge action combined with the standard Wilson quark is
presented for the case of $N_F=2$: With this action the finite temperature
transition is shown to be continuous in the chiral limit confirming the result
of the standard action. Furthermore, not like the case of the standard action
where lattice artifacts make the transition once very strong at intermediate
values of the hopping parameter $K$ on $N_t=4$ and 6 lattices, a smooth
crossover is found for the improved action when we increase $1/K-1/K_c$, in
accord with a naive expectation about the fate of second order chiral
transition at finite $m_q$.


title: Determination of the renormalized heavy-quark mass in Lattice QCD

abstract:
  We study on the lattice the correlator of heavy-quark currents in the
vicinity of vanishing momentum. The renormalized charmed quark mass, the
renormalized strong coupling constant and gluon condensate can be defined in
terms of the derivatives of that correlator at zero momentum. We analyze
quenched Monte-Carlo data on a small lattice $8^3*16$ for $\beta=6$. We
generalize dispersion relations to the lattice theory in a simple way and use
them successfully to fit the correlator at both small and large distances. We
fit the short-distance part of the correlator with the relevant expressions of
perturbative QCD on the lattice and obtain the value of the renormalized quark
mass $m_c^{\bar{MS}}(m_c)\,=\,1.20(4)\,GeV$.


title: Monopoles in Compact U(1) -- Anatomy of the Phase Transition

abstract:
  We present evidence that the existence of a first order phase transition in
compact U(1) with Wilson action is not related to monopole loops wrapping
around the toroidal lattice, as has been previously suggested. Our analysis is
based on the suppression of such loops by `soft boundary conditions' that
correspond to an infinitely large chemical potential for the monopoles on the
boundary, during the updating process. It is observed that the double peak
structure characteristic for the first order phase transition reappears at
sufficiently large lattice sizes and separations from the lattice boundary.


title:
New extended high temperature series for the N-vector spin models on
  three-dimensional bipartite lattices

abstract:
  High temperature expansions for the susceptibility and the second correlation
moment of the classical N-vector model (O(N) symmetric Heisenberg model) on the
sc and the bcc lattices are extended to order $\beta^{19}$ for arbitrary N. For
N= 2,3,4.. we present revised estimates of the critical parameters from the
newly computed coefficients.


title: Full QCD with the L\"uscher local bosonic action

abstract:
  We investigate L\"uscher's method of including dynamical Wilson fermions in a
lattice simulation of QCD with two quark flavours. We measure the accuracy of
the approximation by comparing it with Hybrid Monte Carlo results for gauge
plaquette and Wilson loops. We also introduce an additional global Metropolis
step in the update. We show that the complexity of L\"uscher's algorithm
compares favourably with that of the Hybrid Monte Carlo.


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

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


title:
Reply to David's Comment on ``Superinstantons and the Reliability of
  Perturbation Theory in Non-Abelian Models''

abstract:
  We reply to David's comment (hep-lat/9504017) on our paper Phys.Rev.Lett.
74(1995)1920.


title: Chiral Phase Transition at Strong Coupling in Lattice QCD

abstract:
  We study the chiral phase transition with staggered fermions on the lattice
at finite temperature in the strong coupling limit. The thermodynamic potential
is derived in the large $d$ approximation where $d+1$ is the dimension of space
time. Our calculation is simpler than the conventional method and leads to a
simple physical interpretation for the approximation scheme.


title:
A Class of Saddle-point Configurations in three-dimensional SU(2)
  Lattice Gauge Theory

abstract:
  We discuss a class of saddle-point configurations in SU(2) lattice gauge
theory in three Euclidean dimensions. These configurations are smooth on the
scale of the lattice and have an action density exhibiting localized peaks, as
has been seen in cooled and extremized Monte Carlo generated lattices. Large
Wilson loops centered on the action peaks show a unit of Z(2) flux. We discuss
the generation of these configurations and measurements of the Creutz ratios on
them.


title: On the chiral limit in lattice gauge theories with Wilson fermions

abstract:
  The chiral limit $~\kappa \simeq \kappa_c(\beta)~$ in lattice gauge theories
with Wilson fermions and problems related to near--to--zero ('exceptional')
eigenvalues of the fermionic matrix are studied. For this purpose we employ
compact lattice QED in the confinement phase. A new estimator $~\mpr_{\pi}~$
for the calculation of the pseudoscalar mass $~m_{\pi}~$ is proposed which does
not suffer from 'divergent' contributions at $\kappa \simeq \kappa_c(\beta)$.
We conclude that the main contribution to the pion mass comes from larger
modes, and 'exceptional' eigenvalues play {\it no} physical role. The behaviour
of the subtracted chiral condensate $~\langle \psb \psi \rangle_{subt}~$ near
$~\kappa_c(\beta)~$ is determined. We observe a comparatively large value of
$~\langle \psb \psi \rangle_{subt} \cdot Z_P^{-1}~$, which could be interpreted
as a possible effect of the quenched approximation.


title: A Swendsen-Wang update algorithm for the Symanzik improved sigma model

abstract:
  We study a generalization of Swendsen-Wang algorithm suited for Potts models
with next-next-neighborhood interactions. Using the embedding technique
proposed by Wolff we test it on the Symanzik improved bidimensional non-linear
$\sigma$ model. For some long range observables we find a little slowing down
exponent ($z \simeq 0.3$) that we interpret as an effect of the partial
frustration of the induced spin model.


title: Lattice energy-momentum tensor with Symanzik improved actions

abstract:
  We define the energy-momentum tensor on lattice for the $\lambda \phi^4$ and
for the nonlinear $\sigma$-model Symanzik tree-improved actions, using Ward
identities or an explicit matching procedure. The resulting operators give the
correct one loop scale anomaly, and in the case of the sigma model they can
have applications in Monte Carlo simulations.


title: Is the Quenched Spectrum in agreement with Experiment?

abstract:
  We analyse the meson spectrum in quenched QCD using lattice gauge theory. By
studying hadron propagation with a variety of operators (both smeared and
local), we are able to extract the ground state and first excited state masses
with confidence. We pay attention to the correlations among the data used in
the fits to extract these masses and couplings. We compare the resulting hadron
spectrum with experiment and find evidence for a significant departure in the
pseudoscalar and vector meson masses.


title: A Cluster Algorithm for the $Z_2$ Kalb-Ramond Model

abstract:
  A cluster algorithm is presented for the $Z_2$ Kalb-Ramond plaquette model in
four dimensions which dramatically reduces critical slowing. The critical
exponent $z$ is reduced from $ z>2$ (standard Metropolis algorithm) to $z=
0.32\pm0.06$. The Cluster algorithm updates the monopole configuration known to
be responsible for the second order phase transition.


title:
SPHERICALLY SYMMETRIC RANDOM WALKS I. REPRESENTATION IN TERMS OF
  ORTHOGONAL POLYNOMIALS

abstract:
  Spherically symmetric random walks in arbitrary dimension $D$ can be
described in terms of Gegenbauer (ultraspherical) polynomials. For example,
Legendre polynomials can be used to represent the special case of
two-dimensional spherically symmetric random walks. In general, there is a
connection between orthogonal polynomials and semibounded one-dimensional
random walks; such a random walk can be viewed as taking place on the set of
integers $n$, $n=0,~1,~2,~\ldots$, that index the polynomials. This connection
allows one to express random-walk probabilities as weighted inner products of
the polynomials. The correspondence between polynomials and random walks is
exploited here to construct and analyze spherically symmetric random walks in
$D$-dimensional space, where $D$ is {\sl not} restricted to be an integer. The
weighted inner-product representation is used to calculate exact closed-form
spatial and temporal moments of the probability distribution associated with
the random walk. The polynomial representation of spherically symmetric random
walks is also used to calculate the two-point Green's function for a
rotationally symmetric free scalar quantum field theory.


title:
SPHERICALLY SYMMETRIC RANDOM WALKS II. DIMENSIONALLY DEPENDENT CRITICAL
  BEHAVIOR

abstract:
  A recently developed model of random walks on a $D$-dimensional
hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is
extended to include the possibility of creating and annihilating random
walkers. Steady-state distributions of random walkers are obtained for all
dimensions $D>0$ by solving a discrete eigenvalue problem. These distributions
exhibit dimensionally dependent critical behavior as a function of the birth
rate. This remarkably simple model exhibits a second-order phase transition
with a nontrivial critical exponent for all dimensions $D>0$.


title:
SPHERICALLY SYMMETRIC RANDOM WALKS III. POLYMER ADSORPTION AT A
  HYPERSPHERICAL BOUNDARY

abstract:
  A recently developed model of random walks on a $D$-dimensional
hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is
used to study polymer growth near a $D$-dimensional attractive hyperspherical
boundary. The model determines the fraction $P(\kappa)$ of the polymer adsorbed
on this boundary as a function of the attractive potential $\kappa$ for all
values of $D$. The adsorption fraction $P(\kappa)$ exhibits a second-order
phase transition with a nontrivial scaling coefficient for $0<D<4$, $D\neq 2$,
and exhibits a first-order phase transition for $D>4$. At $D=4$ there is a
tricritical point with logarithmic scaling. This model reproduces earlier
results for $D=1$ and $D=2$, where $P(\kappa)$ scales linearly and
exponentially, respectively. A crossover transition that depends on the radius
of the adsorbing boundary is found.


title: Universality in Random Walk Models with Birth and Death

abstract:
  Models of random walks are considered in which walkers are born at one
location and die at all other locations with uniform death rate. Steady-state
distributions of random walkers exhibit dimensionally dependent critical
behavior as a function of the birth rate. Exact analytical results for a
hyperspherical lattice yield a second-order phase transition with a nontrivial
critical exponent for all positive dimensions $D\neq 2,~4$. Numerical studies
of hypercubic and fractal lattices indicate that these exact results are
universal. Implications for the adsorption transition of polymers at curved
interfaces are discussed.


title: Lattice fermions with gauge noninvariant measure

abstract:
  We define Weyl fermions on a finite lattice in such a way that in the path
integral the action is gauge invariant but the functional measure is not. Two
variants of such a formulation are tested in perturbative calculation of the
fermion determinant in chiral Schwinger model. We find that one of these
variants ensures restoring the gauge invariance of the nonanomalous part of the
determinant in the continuum limit. A `perfect' perturbative regularization of
the chiral fermions is briefly discussed.


title: Monopole Condensation in Lattice SU(2) QCD

abstract:
  This is the short review of Monte-Carlo studies of quark confinement in
lattice QCD. After abelian projections both in the maximally abelian and
Polyakov gauges, it is seen that the monopole part alone is responsible for
confinement. A block spin transformation on the dual lattice suggests that
lattice $SU(2)$ QCD is always ( for all $\beta$) in the monopole condensed
phase and so in the confinement phase in the infinite volume limit.


title:
Quark-Antiquark Forces From SU(2) and SU(3) Gauge Theories on Large
  Lattices

abstract:
  We present results on the spin-independent quark-antiquark potential in SU(3)
gauge theory from a simulation on a 48^3*64 lattice at Beta = 6.8,
corresponding to a volume of (1.7 fm)^3. Moreover, a comprehensive analysis of
spin- and velocity-dependent potentials is carried out for SU(2) gauge theory,
with emphasis on the short range structure, on lattices with resolutions
ranging from .02 fm to .04 fm.


title: Dual Abrikosov Vortices in Confining Theories

abstract:
  The spacial distribution of fields and currents in confining theories can
give direct evidence of dual superconductivity. We would like to discuss the
techniques for finding these properties and calculating the superconductivity
parameters in lattice simulations. We have seen dual Abrikosov vortices
directly in pure U(1) and SU(2) and others have also seen them in SU(3). In the
non-Abelian cases the system appears to be near the borderline between type I
and II. We also discuss the response of the supercurrents to external fields.


title:
Variational Study of the Phase Transition at Finite T in the $\lambda
  \phi^4 $-Theory

abstract:
  Assuming triviality of the 4-dimensional $\lambda \phi ^4$-theory we compute
the effective potential by means of a self consistent Feynman-Bogoliubov
method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by
a stability condition for the gap-equation for the plasma mass. It shows a
second order phase transition at zero temperature, in agreement with a large
amount of analytical and RG analysis as well as Monte Carlo numerical evidence.
As the cutoff $\Lambda $ is removed the renormalized self coupling constant
$\lambda _R$ goes to zero consistent with the claim of triviality. At finite
temperature the phase transition becomes weakly first order.


title:
Kramers equation algorithm for simulations of QCD with two flavors of
  Wilson fermions and gauge group SU(2)

abstract:
  We compare the Hybrid Monte Carlo (HMC) and the Kramers equation algorithms
for simulations of QCD with two flavors of dynamical Wilson fermions and gauge
group $SU(2)$. The results for the performance of both algorithms are obtained
on $6^312$, $12^4$ and $16^4$ lattices at a pion to $\rho$ meson mass ratio of
$m_\pi/m_\rho \approx 0.9$. We find that the Kramers equation algorithm gives
an equally good performance as the HMC algorithm. We demonstrate that the
classical equations of motion used in these algorithms lack reversibility in
practical simulations and behave like those of a chaotic dynamical system with
a Liapunov exponent $\nu \approx 0.75$.


title:
Deep Inelastic Scattering in Improved Lattice QCD. II. The second moment
  of structure functions

abstract:
  In this paper we present the 1-loop perturbative computation of the
renormalization constants and mixing coefficients of the lattice quark
operators of rank three whose hadronic elements enter in the determination of
the second moment of Deep Inelastic Scattering (DIS) structure functions.
  We have employed in our calculations the nearest-neighbor improved
``clover-leaf'' 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
demonstrated to be absent from on-shell hadronic lattice matrix elements. We
have limited our computations to the quenched case, in which quark operators do
not mix with gluon operators.
  We have studied the transformation properties under the hypercubic group of
the operators up to the rank five (which are related to moments up to the
fourth of DIS structure functions), and we discuss the choice of the operators
considered in this paper together with the feasibility of lattice computations
for operators of higher ranks.
  To perform the huge amount of calculations required for the evaluation of all
the relevant Feynman diagrams, we have extensively used the symbolic
manipulation languages Schoonschip and Form.


title: Square Gravity

abstract:
  We simulate the Ising model on dynamical quadrangulations using a
generalization of the flip move for triangulations with two aims: firstly, as a
confirmation of the universality of the KPZ/DDK exponents of the Ising phase
transition, worthwhile in view of some recent surprises with other sorts of
dynamical lattices; secondly, to investigate the transition of the Ising
antiferromagnet on a dynamical loosely packed (bipartite) lattice. In the
latter case we show that it is still possible to define a staggered
magnetization and observe the antiferromagnetic analogue of the transition.


title:
3-D lattice simulation of the electroweak phase transition at small
  Higgs mass

abstract:
  We study the electroweak phase transition by lattice simulations of an
effective 3-dimensional theory, for a Higgs mass of about $35 GeV$. In the
broken symmetry phase our results on masses and the Higgs condensate are
consistent with 2-loop perturbative results. However, we find a
non-perturbative lowering of the transition temperature, similar to the one
previously found at $m_H = 80 GeV$. For the symmetric phase, bound state masses
and the static force are determined and compared with results for pure $SU(2)$
theory.


title: Gluon Propagators and Confinement

abstract:
  We present SU(3) gluon propagators calculated on 48*48*48*N_t lattices at
beta=6.8 where N_t=64 (corresponding the confinement phase) and N_t=16
(deconfinement) with the bare gauge parameter,alpha, set to be 0.1. In order to
avoid Gribov copies, we employ the stochastic gauge fixing algorithm. Gluon
propagators show quite different behavior from those of massless gauge fields:
(1) In the confinement phase, G(t) shows massless behavior at small and large
t, while around 5<t<15 it behaves as massive particle, and (2) effective mass
observed in G(z) becomes larger as z increases. (3) In the deconfinement phase,
G(z) shows also massive behavior but effective mass is less than in the
confinement case. In all cases, slope masses are increasing functions of t or
z, which can not be understood as addtional physical poles.


title: Equation of State for the SU(3) Gauge Theory

abstract:
  Through a detailed investigation of the $SU(3)$ gauge theory at finite
temperature on lattices of various size we can control finite lattice cut-off
effects in bulk thermodynamic quantities. We calculate the pressure and energy
density of the $SU(3)$ gauge theory on lattices with temporal extent $N_\tau =
4$, 6 and 8 and spatial extent $N_\sigma =16$ and 32. The results are
extrapolated to the continuum limit. We find a deviation from ideal gas
behaviour of (15-20)\%, depending on the quantity, even at temperatures as high
as $T\sim 3T_c$. A calculation of the critical temperature on lattices with
temporal extent $N_\tau = 8$ and 12 and the string tension on $32^4$ lattices
at the corresponding critical couplings is performed to fix the temperature
scale. An extrapolation to the continuum limit yields $T_c/\sqrt{\sigma} =
0.629(3)$.


title: Precision Charmonium Spectroscopy From Lattice QCD

abstract:
  We present 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 with
tadpole-improved coefficients. We use multi-exponential fits to multiple
correlation functions to extract ground and excited $S$ states. Splittings
between the lowest $S$, $P$ and $D$ states are given and we have accurate
values for the $S$ state hyperfine splitting and the $\chi_c$ fine structure.
Agreement with experiment is good - the remaining systematic errors are
discussed.


title: The $\bar{s}s$ content of the D-meson at infinite coupling

abstract:
  We calculate the $\bar{s}s$ condensate in the D - and B - mesons using the
unquenched hopping parameter expansion at infinite coupling for the Wilson
lattice action. We discuss the phenomenological relevance of our result.


title: Strong Coupling Lattice Schwinger Model on Large Spherelike Lattices

abstract:
  The lattice regularized Schwinger model for one fermion flavor and in the
strong coupling limit is studied through its equivalent representation as a
restricted 8-vertex model. The Monte Carlo simulation on lattices with
torus-topology is handicapped by a severe non-ergodicity of the updating
algorithm; introducing lattices with spherelike topology avoids this problem.
We present a large scale study leading to the identification of a critical
point with critical exponent $\nu=1$, in the universality class of the Ising
model or, equivalently, the lattice model of free fermions.


title: Interface Tension of the Electroweak Phase Transition

abstract:
  In our nonperturbative lattice investigation we study the interface tension
of the finite-temperature electroweak phase transition. In this analysis the
Higgs mass has been chosen to be about $35$ GeV. At the transition point of a
finite volume system, tunnelling between the symmetric and the Higgs phase
takes place. This phenomenon leads to a splitting of the ground state, which
can be used to determine the interface tension. The result obtained this way
agrees with the result of the two-coupling method and with the prediction of
the perturbative approach.


title: The classically perfect fixed point action for SU(3) gauge theory

abstract:
  In this paper (the first of a series) we describe the construction of fixed
point actions for lattice $SU(3)$ pure gauge theory. Fixed point actions have
scale invariant instanton solutions and the spectrum of their quadratic part is
exact (they are classical perfect actions). We argue that the fixed point
action is even 1--loop quantum perfect, i.e. in its physical predictions there
are no $g^2 a^n$ cut--off effects for any $n$. We discuss the construction of
fixed point operators and present examples. The lowest order $q {\bar q}$
potential $V(\vec{r})$ obtained from the fixed point Polyakov loop correlator
is free of any cut--off effects which go to zero as an inverse power of the
distance $r$.


title: Non--perturbative tests of the fixed point action for SU(3) gauge theory

abstract:
  In this paper (the second of a series) we extend our calculation of a
classical fixed point action for lattice $SU(3)$ pure gauge theory to include
gauge configurations with large fluctuations. The action is parameterized in
terms of closed loops of link variables. We construct a few-parameter
approximation to the classical FP action which is valid for short correlation
lengths. We perform a scaling test of the action by computing the quantity $G =
L \sqrt{\sigma(L)}$ where the string tension $\sigma(L)$ is measured from the
torelon mass $\mu = L \sigma(L)$. We measure $G$ on lattices of fixed physical
volume and varying lattice spacing $a$ (which we define through the
deconfinement temperature). While the Wilson action shows scaling violations of
about ten per cent, the approximate fixed point action scales within the
statistical errors for $ 1/2 \ge aT_c \ge 1/6$. Similar behaviour is found for
the potential measured in a fixed physical volume.


title:
The absence of cut--off effects for the fixed point action in 1--loop
  perturbation theory

abstract:
  In order to support the formal renormalization group arguments that the fixed
point action of an asymptotically free model gives cut--off independent
physical predictions in 1--loop perturbation theory, we calculate the finite
volume mass--gap $m(L)$ in the non--linear $\sigma$--model. No cut--off effect
of the type $g^4\left(a/L\right)^n$ is seen for any $n$. The results are
compared with those of the standard and tree level improved Symanzik actions.


title: On the Structure of the Yang-Mills Vacuum

abstract:
  In this talk I will discuss the current picture of color confinement. In
particular, I will show how it can be tested microscopically. It is stressed
that the color magnetic monopoles in this picture are dyons. Furthermore, the
role of instantons is illuminated.


title:
Exact Matching Condition for Matrix Elements in Lattice and
  $\overline{MS}$ Schemes

abstract:
  The exact matching condition is given for hadron matrix elements calculated
in any two different schemes, in particular, in the lattice and dimensional
regularization, (modified) minimal subtraction $\overline{\rm MS}$ schemes. The
result provides insight into and permits to go beyond Lepage and Mackenzie's
mean field theory of removing tadpole contributions in lattice operators.


title:
Investigating Yang-Mills theory and Confinement as a function of the
  spatial volume

abstract:
  We study the volume dependence of electric flux energies for SU(2) gauge
theory with twisted boundary conditions. The curves interpolate smoothly
between the perturbative semiclassicalresults and the Confinement regime. On
the basis of our results, we propose that the Confinement property might be
caused by a class of non-dilute multi-instanton configurations.


title:
Weak Decays of Heavy-Light Mesons on the Lattice: Semi-Leptonic
  Formfactors

abstract:
  We report results (on an intermediate statistics sample) of a study of weak
semi-leptonic formfactors of $B$ and $D$ decays, addressing the uncertainties
from mass extrapolations to chiral and to heavy quarks. Moreover, we present a
nonperturbative test to the LMK current renormalization scheme for vector
current {\it transition} matrix elements and find remarkable agreement.


title: A class of chiral fermion models

abstract:
  We study the relation between the Roma and Zaragoza proposals for chiral
fermions on the lattice. The fermion action in the Roma approach is shown to be
equivalent to one of the Zaragoza type. This result is used to perform a
mean-field study of the phase diagram for chiral Yukawa models based on the
Roma action. The phase diagram is compared with the one based on the Zaragoza
model with the most local choice for the fermion interactions.


title:
Finite-volume two-pion energies and scattering in the quenched
  approximation

abstract:
  We investigate how L\"uscher's relation between the finite-volume energy of
two pions at rest and pion scattering lengths has to be modified in quenched
QCD. We find that this relation changes drastically, and in particular, that
``enhanced finite-volume corrections" of order $L^0=1$ and $L^{-2}$ occur at
one loop ($L$ is the linear size of the box), due to the special properties of
the $\eta'$ in the quenched approximation. We define quenched pion scattering
lengths, and show that they are linearly divergent in the chiral limit. We
estimate the size of these various effects in some numerical examples, and find
that they can be substantial.


title: On the question of universality in $\RPn$ and $\On$ Lattice Sigma Models

abstract:
  We argue that there is no essential violation of universality in the
continuum limit of mixed $\RPn$ and $\On$ lattice sigma models in 2 dimensions,
contrary to opposite claims in the literature.


title: Gauge invariant structures and Confinement

abstract:
  By looking at cooled configurations on the lattice, we study the presence of
peaks in the action density, or its electric and magnetic components, in the
SU(2) gauge vacuum. The peaks are seen to be of instanton-like nature and their
number variation takes care of the drop in the string tension observed when
cooling. Possible explanations of this finding are analysed.


title: Improving lattice perturbation theory

abstract:
  Lepage and Mackenzie have shown that tadpole renormalization and systematic
improvement of lattice perturbation theory can lead to much improved numerical
results in lattice gauge theory. It is shown that lattice perturbation theory
using the Cayley parametrization of unitary matrices gives a simple analytical
approach to tadpole renormalization, and that the Cayley parametrization gives
lattice gauge potentials gauge transformations close to the continuum form. For
example, at the lowest order in perturbation theory, for SU(3) lattice gauge
theory, at $\beta=6,$ the `tadpole renormalized' coupling $\tilde g^2 = {4\over
3} g^2,$ to be compared to the non-perturbative numerical value $\tilde g^2 =
1.7 g^2.$


title: O(N) and RP^{N-1} Models in Two Dimensions

abstract:
  I provide evidence that the 2D $RP^{N-1}$ model for $N \ge 3$ is equivalent
to the $O(N)$-invariant non-linear $\sigma$-model in the continuum limit. To
this end, I mainly study particular versions of the models, to be called
constraint models. I prove that the constraint $RP^{N-1}$ and $O(N)$ models are
equivalent for sufficiently weak coupling. Numerical results for their
step-scaling function of the running coupling $\bar{g}^2= m(L) L$ are
presented. The data confirm that the constraint $O(N)$ model is in the samei
universality class as the $O(N)$ model with standard action. I show that the
differences in the finite size scaling curves of $RP^{N-1}$i and $O(N)$ models
observed by Caracciolo et al. can be explained as a boundary effect. It is
concluded, in contrast to Caracciolo et al., that $RP^{N-1}$ and $O(N)$ models
share a unique universality class.


title:
Two-Dimensional 8-State Potts Model on Random Lattices: A Monte Carlo
  Study

abstract:
  We use two-dimensional Poissonian random lattices of Voronoi/ Delaunay type
to study the effect of quenched coordination number randomness on the nature of
the phase transition in the eight-state Potts model, which is of first order on
regular lattices. From extensive Monte Carlo simulations we obtain strong
evidence that the phase transition remains first order for this type of
quenched randomness. Our result is in striking contrast to a recent Monte Carlo
study of quenched bond randomness for which the order of the phase transition
changes from first to second order.


title: Lattice QCD on Small Computers

abstract:
  We demonstrate that lattice QCD calculations can be made $10^3$--$10^6$ times
faster by using very coarse lattices. To obtain accurate results, we replace
the standard lattice actions by perturbatively-improved actions with
tadpole-improved correction terms that remove the leading errors due to the
lattice. To illustrate the power of this approach, we calculate the
static-quark potential, and the charmonium spectrum and wavefunctions using a
desktop computer. We obtain accurate results that are independent of the
lattice spacing and agree well with experiment.


title: High temperature critical O(N) field models by LCE series

abstract:
  The critical properties of renormalizable O(N) field models are determined by
means of the high order ($\geq 18$) behaviour of convergent linked cluster
series on finite temperature lattices. It is shown that those models become
weakly coupled at the phase transition. The critical exponents agree to those
of the corresponding superrenormalizable 3-dimensional models. Concerning
critical amplitudes and subcritical behaviour, corrections induced by
renormalizable couplings are measurable.


title:
Phase Transitions at Finite Temperature and Dimensional Reduction for
  Fermions and Bosons

abstract:
  In a recent Letter we discussed the fact that large-$N$ expansions and
computer simulations indicate that the universality class of the finite
temperature chiral symmetry restoration transition in the 3D Gross-Neveu model
is mean field theory. This was seen to be a counterexample to the standard
'sigma model' scenario which predicts the 2D Ising model universality class. In
this article we present more evidence, both theoretical and numerical, that
this result is correct. We develop a physical picture for our results and
discuss the width of the scaling region (Ginzburg criterion), $1/N$
corrections, and differences between the dynamics of BCS superconductors and
Gross-Neveu models. Lattices as large as $12 \times 72^2$ are simulated for
both the $N=12$ and $N=4$ cases and the numerical evidence for mean field
scaling is quite compelling. We point out that the amplitude ratio for the
model's susceptibility is a particulartly good observable for distinguishing
between the dimensional reduction and the mean field scenerios, because this
universal quantity differs by almost a factor of $20$ in the two cases. The
simulations are done close to the critical point in both the symmetric and
broken phases, and correlation lengths of order $10$ are measured. The critical
indices $\beta_{mag}$ and $\delta$ also pick out mean field behavior. We trace
the breakdown of the standard scenario (dimensional reduction and universality)
to the composite character of the mesons in the model. We point out that our
results should be generic for theories with dynamical symmetry breaking, such
as Quantum Chromodynamics.
  We also simulated the $O(2)$ model on $8 \times 16^3$ lattices to establish
that our methods give the results of dimensional reduction in purely bosonic


title: The overlap is not a waveguide

abstract:
  Golterman and Shamir falsely claim that a waveguide model modified by adding
many charged bosonic spinors, in the limit of an infinite number of matter
fields, becomes identical to the overlap if in the target theory every fermion
appears in four copies. Their modified model would give wrong results even in
the vectorial four flavor massless Schwinger model, while a dynamical
simulation of this model with the overlap works correctly. In this note we
pinpoint the error in the derivation of Golterman and Shamir.


title: On the fractal structure of two-dimensional quantum gravity

abstract:
  We provide evidence that the Hausdorff dimension is 4 and the spectral
dimension is 2 for two-dimensional quantum gravity coupled the matter with a
central charge $c \leq 1$. For $c > 1$ the Hausdorff dimension and the spectral
dimension monotonously decreases to 2 and 1, respectively.


title: Monte Carlo Study of the Yukawa Coupled Two Spin Ising Model

abstract:
  We consider a particular 4 state spin system composed of two Ising spins
(~$s_x, \; \sigma_x$~) with independent hopping parameters $\kappa_1,
\kappa_2$, coupled by a bilinear Yukawa term, $y s_x \sigma_x$. The Yukawa term
is solely responsible for breaking the global $ Z_2 \times Z_2$ symmetry down
to $Z_2$. This model is intended as an illustration of general coupled Higgs
system where scalars can arise both as composite and elementary excitations.
For the Ising example in 2d, we give convincing numerical evidence of the
universality of the two spin system with the one spin Ising model, by Monte
Carlo simulations and finite scaling analysis . We also show that as we
approach the phase transition, universality arises by a separation of low mass
spin waves from an extra set of spin waves with an energy gap that diverges as
the correlations length diverges


title:
Evidence for Complex Subleading Exponents from the High-Temperature
  Expansion of the Hierarchical Ising Model

abstract:
  Using a renormalization group method, we calculate 800 high-temperature
coefficients of the magnetic susceptibility of the hierarchical Ising model.
The conventional quantities obtained from differences of ratios of coefficients
show unexpected smooth oscillations with a period growing logarithmically and
can be fitted assuming corrections to the scaling laws with complex exponents.


title: A note on the lattice Dirac-Kaehler equation

abstract:
  A lattice version of the Dirac-Kaehler equation (DKE) describing fermions was
discussed in articles by Becher and Joos. The decomposition of lattice
Dirac-Kaehler fields (inhomogeneous cochains) to lattice Dirac fields remained
as an open problem. I show that it is possible to extract Dirac fields from the
DKE and discuss the resulting lattice Dirac equation.


title:
Super-Instantons, Perfect Actions, Finite Size Scaling and the Continuum
  Limit

abstract:
  We discuss some aspects of the continuum limit of some lattice models, in
particular the $2D$ $O(N)$ models. The continuum limit is taken either in an
infinite volume or in a box whose size is a fixed fraction of the infinite
volume correlation length. We point out that in this limit the fluctuations of
the lattice variables must be $O(1)$ and thus restore the symmetry which may
have been broken by the boundary conditions (b.c.). This is true in particular
for the so-called super-instanton b.c. introduced earlier by us. This
observation leads to a criterion to assess how close a certain lattice
simulation is to the continuum limit and can be applied to uncover the true
lattice artefacts, present even in the so-called 'perfect actions'. It also
shows that David's recent claim that super-instanton b.c. require a different
renormalization must either be incorrect or an artefact of perturbation theory.


title:
On behaviour of critical lines near ferrimagnetic phase in Higgs-Yukawa
  systems

abstract:
  We calculate within a mean-field approximation the slopes of the critical
lines near the point of appearing the ferrimagnetic phase for the U(1) systems
in the weak coupling regime. It is demonstrated that the slope of one of the
critical line is continuous, while change of the slope of the other depends
strongly on the number of the fermion flavours. We also find that in the
ferrimagnetic phase near such a point the magnetization and the staggered
magnetization align orthogonally to each other.


title:
The bermions: an approach to lattice QCD dynamical fermions from
  negative flavour numbers

abstract:
  We estimate the effects of dynamical fermions by extrapolating to positive
flavour numbers the results from negative values obtained by adding to the pure
gauge sector a fermion action where the fields obey a Bose statistics: the
bermions.


title: Hyper-Systolic Parallel Computing

abstract:
  A new class of parallel algorithms is introduced that can achieve a
complexity of O(n^3/2) with respect to the interprocessor communication, in the
exact computation of systems with pairwise mutual interactions of all elements.
Hitherto, conventional methods exhibit a communicational complexity of O(n^2).
The amount of computation operations is not altered for the new algorithm which
can be formulated as a kind of h-range problem, known from the mathematical
field of Additive Number Theory. We will demonstrate the reduction in
communicational expense by comparing the standard-systolic algorithm and the
new algorithm on the connection machine CM5 and the CRAY T3D. The parallel
method can be useful in various scientific and engineering fields like exact
n-body dynamics with long range forces, polymer chains, protein folding or
signal processing.

categories: hep-lat astro-ph chem-ph comp-gas cond-mat nlin.CG