title: Properties of B-Mesons in Lattice QCD

abstract:
  The results of an extensive study of B-meson properties in quenched lattice
QCD are presented. The studies are carried out in the static quark limit where
the b-quark is taken to be infinitely massive. Our computations rely on a
multistate smearing method introduced previously, with smearing functions
generated from a relativistic lattice quark model. Systematic errors arising
from excited state contamination, finite volume effects, and the chiral
extrapolation for the light quarks are estimated. We obtain continuum results
for the mass splitting M_{B_s}- M_{B_u} = 86 (+/-)12(stat) {+7/-9}(syst) MeV,
the ratio of decay constants f_{B_s}/f_{B_u} = 1.22 (+/-)0.04(stat) (+/-)0.02
(syst). For the B-meson decay constant we separately exhibit the sizable
uncertainties in the extrapolation to the continuum limit a -> 0 and higher
order perturbative matching. We obtain f_{B} = 188 (+/-)23(stat) (+/-)15(syst)
{+26/-0}(extrap) (+/-)14 (pert) MeV. ----- [Postscript version of paper
available by anonymous ftp at fncrd6.fnal.gov. The file is fb.ps in
subdirectory theory.]


title:
Heating and small-size instantons in the $O(3) \:\sigma$ model on the
  lattice

abstract:
  We study the role of small-size instantons in the determination of the
topological susceptibility of the 2-d $O(3) \: \sigma $ model on the lattice.
In particular, we analyze how they affect the non-perturbative determination,
by Monte Carlo techniques, of the renormalizations on the lattice. As a result,
we obtain a high-precision non-perturbative determination of the mixing with
the unity operator, finding good agreement with perturbative computations. We
also obtain the size distribution of instantons in the physical vacuum up to
very small values of the size in physical units, without observing any
ultraviolet cut-off. Moreover, we show by analytical calculation that the
mixing of the topological susceptibility with the action density is a
negligible part of the whole non-perturbative signal.


title: Beautiful Baryons from Lattice QCD

abstract:
  We perform a lattice study of heavy baryons, containing one ($\Lambda_b$) or
two $b$-quarks ($\Xi_b$). Using the quenched approximation we obtain for the
mass of $\Lambda_b$ $$ M_{\Lambda_b}= 5.728 \pm 0.144 \pm 0.018 {\rm GeV}.$$
The mass splitting between the $\Lambda_b$ and the B-meson is found to increase
by about 20\% if the light quark mass is varied from the chiral limit to the
strange quark mass.


title:
Non perturbative determination of the running coupling constant in
  quenched SU(2)

abstract:
  Through a finite size renormalization group technique we calculate the
running coupling constant for quenched SU(2) with a few percent error over a
range of energy varying by a factor thirty. The definition is based on ratio of
correlations of Polyakov loops with twisted boundary conditions. The
extrapolation to the continuum limit is governed by corrections due to lattice
artifacts which are proportional to the square of the lattice spacing and
appears rather smooth.


title:
Supersymmetric corrections to $\epsilon^\prime /\epsilon at the leading
  order in QCD and QED

abstract:
  We study the corrections to $\epsilon^\prime /\epsilon$ in the minimal
supersymmetric model at the leading order in QCD and QED. Supersymmetry can
increase the standard model prediction for $\epsilon^\prime /\epsilon$ by at
most 40\% for $m_t=174$ GeV, an enhancement which is indistinguishable from the
present theoretical uncertainties. The most conspicuous effect of supersymmetry
is a strong depletion of $\epsilon^\prime /\epsilon$. For certain choices of
supersymmetric parameters, vanishing and even small negative values of
$\epsilon^\prime /\epsilon$ can be obtained for the top quark in the CDF range.


title:
Reply to M.Campostrini's and P.Rossi's Comment on our paper
  `Nonuniformity of the $1/N$ Expansion for Two-Dimensional $O(N)$ Models'

abstract:
  This reply tries to rectify some misunderstandings that are in our opinion
contained in the Comment by Campostrini and Rossi, <hep-lat 99407008> on our
paper <hep-lat 9407003>.


title:
Chiral perturbation theory, finite size effects and the
  three-dimensional $XY$ model

abstract:
  We study finite size effects of the d=3 $XY$ model in terms of the chiral
perturbation theory. We calculate by Monte Carlo simulations physical
quantities which are, to order of $(1/L)^2$, uniquely determined only by two
low energy constants. They are the magnetization and the helicity modulus (or
the Goldstone boson decay constant) in infinite volume. We also pay a special
attention to the region of the validity of the two possible expansions in the
theory.


title: Pion-Nucleon Sigma Term in Lattice QCD

abstract:
  We calculate both connected and disconnected contribution to the $\pi$-$N$
$\sigma$-term in quenched lattice QCD with Wilson quark action on a $12^3\times
20$ lattice at $\beta=5.7$. The latter is evaluated with the aid of the variant
wall source method, which was previously applied successfully for extraction of
$\pi$-$\pi$ scattering lengths and $\eta^\prime$ meson mass. We found that the
disconnected contribution is about twice larger than the connected one. The
value for the full $\pi$-$N$ $\sigma$ term $\sigma=40-60$ MeV is consistent
with the experimental estimates. The nucleon matrix element of the strange
quark density $\bar s s$ is fairly large in our result.


title: Polyakov loops and monopoles in QCD

abstract:
  Monte-Carlo simulations of abelian projection of $T \neq 0$ pure lattice QCD
show that 1) Polyakov loops written in terms of abelian link fields alone play
a role of an order parameter of deconfinement transition, 2) the abelian
Polyakov loops are decomposed into contributions from Dirac strings of
monopoles and from photons, 3) vanishing of the abelian Polyakov loops in the
confinement phase is due to the Dirac strings alone and the photons give a
finite contribution in both phases. Moreover, these results appear to hold good
with any abelian projection as seen from the studies in the maximally abelian
gauge and in various unitary gauges.


title: Monopole action and condensation in SU(2) QCD

abstract:
  An effective monopole action for various extended monopoles is derived from
vacuum configurations after abelian projection in the maximally abelian gauge
in $SU(2)$ QCD. The action appears to be independent of the lattice volume.
Moreover it seems to depend only on the physical lattice spacing of the
renormalized lattice, not on $\beta$. Entropy dominance over energy of monopole
loops is seen on the renormalized lattice with the spacing $b>b_c\simeq
5.2\times10^{-3} \Lambda_L^{-1}$. This suggests that monopole condensation
always (for all $\beta$) occurs in the infinite-volume limit of lattice QCD.


title: The Sine Gordon Model: Perturbation Theory and Cluster Monte Carlo

abstract:
  We study the expansion of the surface thickness in the 2-dimensional lattice
Sine Gordon model in powers of the fugacity z. Using the expansion to order
z**2, we derive lines of constant physics in the rough phase. We describe and
test a VMR cluster algorithm for the Monte Carlo simulation of the model. The
algorithm shows nearly no critical slowing down. We apply the algorithm in a
comparison of our perturbative results with Monte Carlo data.


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

abstract:
  A preliminary computation of the Isgur-Wise universal form factor using a
lattice formulation of the Heavy Quark Effective Theory (HQET) is described and
compared with the recent data from ARGUS and CLEO on B -> D*lv decay.


title: Nucleon Structure from Lattice QCD

abstract:
  We report results on the nucleon structure obtained from the lattice quantum
chromodynamics calculation. These include the axial, electromagnetic, $\pi NN$,
and scalar form factors. The calculation is carried out at $\beta = 6$ on a
$16^3 \times 24$ lattice with 24 quenched gauge configurations. The chiral
limit results are extrapolated from several light quark cases. For the
disconnected insertion (sea-quark contribution), we used the stochastic
estimation with the $Z_2$ noise to calculate the diagonal and off-diagonal
traces of the inverse matrices with a size of $10^6 \times 10^6$. It is found
that the $Z_2$ noise is the optimal choice and its comparison with the Gaussian
noise for our quark matrix is given. For the sea-quark contribution, we report
results on the strange condensate in the nucleon and the $\pi N \sigma$ term.


title:
Non-Perturbative Renormalization Group Flows in Two-Dimensional Quantum
  Gravity

abstract:
  Recently a block spin renormalization group approach was proposed for the
dynamical triangulation formulation of two-dimensional quantum gravity. We use
this approach to examine non-perturbatively a particular class of higher
derivative actions for pure gravity.


title: Scaling Properties of the Energy Density in SU(2) Lattice Gauge Theory

abstract:
  The lattice data for the energy density of $SU(2)$ gauge theory are
calculated with \nop~derivatives of the coupling constants. These derivatives
are obtained from two sources : i) a parametrization of the \nop~beta function
in accord with the measured critical temperature and $\Delta\beta-$values and
ii) a \nop~calculation of the presssure. We then perform a detailed finite size
scaling analysis of the energy density near $T_c$. It is shown that at the
critical temperature the energy density is scaling as a function of $VT^3$ with
the corresponding $3d$ Ising model critical exponents. The value of
$\epsilon(T_c)/T^4_c$ in the continuum limit is estimated to be 0.256(23). In
the high temperature regime the energy density is approaching its weak coupling
limit from below, at $T/T_c \approx 2$ it has reached only about $70\%$ of the
limit.


title:
"Confinement Mechanism in Various Abelian Projections of $SU(2)$ Lattice
  Gluodynamics"

abstract:
  We show that the monopole confinement mechanism in lattice gluodynamics is a
particular feature of the maximal abelian projection. We give an explicit
example of the $SU(2) \rightarrow U(1)$ projection (the minimal abelian
projection), in which the confinement is due to topological objects other than
monopoles. We perform analytical and numerical study of the loop expansion of
the Faddeev--Popov determinant for the maximal and the minimal abelian
projections, and discuss the fundamental modular region for these projections.


title: Tricritical Phenomena in a Z(3) Lattice Gauge Theory

abstract:
  The Z(3) gauge model with double plaquette representation of the action on a
generalized Bethe lattice of plaquettes is constructed. It is reduced to the
spin-1 Blume-Emery-Griffiths (BEG) model. An Ising-type critical line of a
second-order phase transition ending in the tricritical point is found.


title:
Interrelation of a Z(3) Gauge Theory on the Flat Lattices and a Spin-1
  BEG Model

abstract:
  The Z(3) gauge model with double plaquette representation of the action on
the flat triangular and square lattices is constructed. It is reduced to the
spin-1 Blume-Emery-Griffiths (BEG) model. An Ising-type critical line of a
second-order phase transition is found.


title:
Spectrum of the Dirac Operator and Multigrid Algorithm with Dynamical
  Staggered Fermions

abstract:
  Complete spectra of the staggered Dirac operator $\Dirac$ are determined in
quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of
dynamical fermions.
  Periodic as well as antiperiodic boundary conditions are used.
  An attempt is made to relate the performance of multigrid (MG) and conjugate
gradient (CG) algorithms for propagators with the distribution of the
eigenvalues of~$\Dirac$.
  The convergence of the CG algorithm is determined only by the condition
number~$\kappa$ and by the lattice size.
  Since~$\kappa$'s do not vary significantly when quarks become dynamic,
  CG convergence in unquenched fields can be predicted from quenched
simulations.
  On the other hand, MG convergence is not affected by~$\kappa$ but depends on
the spectrum in a more subtle way.


title: Compact lattice QED with Wilson fermions

abstract:
  We study the phase structure and the chiral limit of $4d$ compact lattice QED
with Wilson fermions (both dynamical and quenched). We use the standard Wilson
gauge action and also a modified one suppressing lattice artifacts. Different
techniques and observables to locate the chiral limit are discussed.


title:
Entropy and the Approach to the Thermodynamic Limit in Three-Dimensional
  Simplicial Gravity

abstract:
  We present numerical results supporting the existence of an exponential bound
in the dynamical triangulation model of three-dimensional quantum gravity.Both
the critical coupling and various other quantities show a slow power law
approach to the infinite volume limit.


title:
The (LATTICE) QCD Potential and Running Coupling: How to Accurately
  Interpolate between Multi-Loop QCD and the String Picture

abstract:
  We present a simple parameterization of a running coupling constant, defined
via the static potential, that interpolates between 2-loop QCD in the UV and
the string prediction in the IR. Besides the usual $\Lam$-parameter and the
string tension, the coupling depends on one dimensionless parameter,
determining how fast the crossover from UV to IR behavior occurs (in principle
we know how to take into account any number of loops by adding more
parameters). Using a new Ansatz for the LATTICE potential in terms of the
continuum coupling, we can fit quenched and unquenched Monte Carlo results for
the potential down to ONE lattice spacing, and at the same time extract the
running coupling to high precision. We compare our Ansatz with 1-loop results
for the lattice potential, and use the coupling from our fits to quantitatively
check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie
estimate of the coupling extracted from the plaquette, and determine Sommer's
scale $r_0$ much more accurately than previously possible. For pure SU(3) we
find that the coupling scales on the percent level for $\beta\geq 6$.


title: Topological Zero Modes in Monte Carlo Simulations

abstract:
  We present an improvement of global Metropolis updating steps, the instanton
hits, used in a hybrid Monte Carlo simulation of the two-flavor Schwinger model
with staggered fermions. These hits are designed to change the topological
sector of the gauge field. In order to match these hits to an unquenched
simulation with pseudofermions, the approximate zero mode structure of the
lattice Dirac operator has to be considered explicitly.


title: Lee-Yang zeroes in the one flavour massive lattice Schwinger model

abstract:
  We study the partition function of the model formulated with Wilson fermions
with only one species, both analytically and numerically. At strong coupling we
construct the solution for lattice size up to $8\times 8$, a polynomial in the
hopping parameter up to $O(\ka^{128})$. At $\be>0$ we evaluate the expectation
value of the fermion determinant for complex values of $\ka$. From the Lee-Yang
zeroes we find support for the existence of a line of phase transitions from
$(\be=0, \ka\simeq 0.38)$ up to $(\be=\infty, \ka=1/4)$.


title:
An Improved Estimator for the Correlation Function of 2D Nonlinear Sigma
  Models

abstract:
  I present a new improved estimator for the correlation function of 2D
nonlinear sigma models. Numerical tests for the 2D XY model and the 2D
O(3)-invariant vector model were performed. For small physical volume, i.e. a
lattice size small compared to the to the bulk correlation length, a reduction
of the statistical error of the finite system correlation length by a factor of
up to 30 compared to the cluster-improved estimator was observed. This
improvement allows for a very accurate determination of the running coupling
proposed by M. L"uscher et al. for 2D O(N)-invariant vector models.


title:
Complex-Temperature Singularities of the Susceptibility in the $d=2$
  Ising Model. I. Square Lattice

abstract:
  We investigate the complex-temperature singularities of the susceptibility of
the 2D Ising model on a square lattice. From an analysis of low-temperature
series expansions, we find evidence that as one approaches the point $u=u_s=-1$
(where $u=e^{-4K}$) from within the complex extensions of the FM or AFM phases,
the susceptibility has a divergent singularity of the form $\chi \sim
A_s'(1+u)^{-\gamma_s'}$ with exponent $\gamma_s'=3/2$. The critical amplitude
$A_s'$ is calculated. Other critical exponents are found to be
$\alpha_s'=\alpha_s=0$ and $\beta_s=1/4$, so that the scaling relation
$\alpha_s'+2\beta_s+\gamma_s'=2$ is satisfied. However, using exact results for
$\beta_s$ on the square, triangular, and honeycomb lattices, we show that
universality is violated at this singularity: $\beta_s$ is lattice-dependent.
Finally, from an analysis of spin-spin correlation functions, we demonstrate
that the correlation length and hence susceptibility are finite as one
approaches the point $u=-1$ from within the symmetric phase. This is confirmed
by an explicit study of high-temperature series expansions.


title:
The High-Temperature Expansion of the Hierarchical Ising Model: From
  Poincar\'e Symmetry to an Algebraic Algorithm

abstract:
  We show that the hierarchical model at finite volume has a symmetry group
which can be decomposed into rotations and translations as the familiar
Poincar\'e groups. Using these symmetries, we show that the intricate sums
appearing in the calculation of the high-temperature expansion of the magnetic
susceptibility can be performed, at least up to the fourth order, using
elementary algebraic manipulations which can be implemented with a computer.
These symmetries appear more clearly if we use the 2-adic fractions to label
the sites. We then apply the new algebraic methods to the calculation of
quantities having a random walk interpretation. In particular, we show that the
probability of returning at the starting point after $m$ steps has poles at
$D=-2,-4,....-2m$ , where $D$ is a free parameter playing a role similar to the
dimensionality in nearest neighbor models.


title: Noncompact Gauge-Invariant Lattice Simulations

abstract:
  We have applied a new gauge-invariant, noncompact, Monte Carlo method to
simulate $U(1)$, $SU(2)$, and $SU(3)$ gauge theories on $8^4$ and $12^4$
lattices. The Creutz ratios of the Wilson loops agree with the exact results
for $U(1)$ for $\beta \ge 1$ apart from a renormalization of the charge. The
$SU(2)$ and $SU(3)$ Creutz ratios robustly display quark confinement at $\beta
= 0.5$ and $\beta = 1.5$, respectively. At much weaker coupling, the $SU(2)$
and $SU(3)$ Creutz ratios agree with perturbation theory after a
renormalization of the coupling constant.


title: Critical exponents of a three dimensional O(4) spin model

abstract:
  By Monte Carlo simulation we study the critical exponents governing the
transition of the three-dimensional classical O(4) Heisenberg model, which is
considered to be in the same universality class as the finite-temperature QCD
with massless two flavors. We use the single cluster algorithm and the
histogram reweighting technique to obtain observables at the critical
temperature. After estimating an accurate value of the inverse critical
temperature $\Kc=0.9360(1)$, we make non-perturbative estimates for various
critical exponents by finite-size scaling analysis. They are in excellent
agreement with those obtained with the $4-\epsilon$ expansion method with
errors reduced to about halves of them.


title: Subtleties and Fancies in Gauge Theory Non Trivial Vacuum

abstract:
  The one loop effective potential for a non-Abelian gauge configuration is
analyzed using the background field method. The Savvidy result and the
non-Abelian ansatz, the other alternative possible background that generates a
constant color magnetic field configuration, are compared. This second
possibility is very interesting because it avoids the possible coordinate
singularity, ${\rm Det}B_i^a=0$, and it is easy to implement in lattice
simulations. We emphasize the interesting dependence of the potential by the
gauge fixing parameter $\alpha$, when the loop expansion is performed around a
non trivial background configuration. Finally, we point out some crucial
differences in analyzing the vacuum structure between non-Abelian gauge
theories and the cases of scalar and Abelian gauge theories.


title:
Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two-
  and Three-Dimensional Self-Avoiding Walks

abstract:
  We make a high-precision Monte Carlo study of two- and three-dimensional
self-avoiding walks (SAWs) of length up to 80000 steps, using the pivot
algorithm and the Karp-Luby algorithm. We study the critical exponents $\nu$
and $2\Delta_4 -\gamma$ as well as several universal amplitude ratios; in
particular, we make an extremely sensitive test of the hyperscaling relation
$d\nu = 2\Delta_4 -\gamma$. In two dimensions, we confirm the predicted
exponent $\nu = 3/4$ and the hyperscaling relation; we estimate the universal
ratios $\<R_g^2\> / \<R_e^2\> = 0.14026 \pm 0.00007$, $\<R_m^2\> / \<R_e^2\> =
0.43961 \pm 0.00034$ and $\Psi^* = 0.66296 \pm 0.00043$ (68\% confidence
limits). In three dimensions, we estimate $\nu = 0.5877 \pm 0.0006$ with a
correction-to-scaling exponent $\Delta_1 = 0.56 \pm 0.03$ (subjective 68\%
confidence limits). This value for $\nu$ agrees excellently with the
field-theoretic renormalization-group prediction, but there is some discrepancy
for $\Delta_1$. Earlier Monte Carlo estimates of $\nu$, which were $\approx\!
0.592$, are now seen to be biased by corrections to scaling. We estimate the
universal ratios $\<R_g^2\> / \<R_e^2\> = 0.1599 \pm 0.0002$ and $\Psi^* =
0.2471 \pm 0.0003$; since $\Psi^* > 0$, hyperscaling holds. The approach to
$\Psi^*$ is from above, contrary to the prediction of the two-parameter
renormalization-group theory. We critically reexamine this theory, and explain
where the error lies.


title: Finite-Size Scaling at $\xi/L \gg 1$

abstract:
  We present a simple and powerful method for extrapolating finite-volume Monte
Carlo data to infinite volume, based on finite-size-scaling theory. We discuss
carefully its systematic and statistical errors, and we illustrate it using
three examples: the two-dimensional three-state Potts antiferromagnet on the
square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $\sigma$-models.
In favorable cases it is possible to obtain reliable extrapolations (errors of
a few percent) even when the correlation length is 1000 times larger than the
lattice.


title: Observing Long Colour Flux Tubes in SU(2) Lattice Gauge Theory

abstract:
  We present results of a high statistics study of the chromo field
distribution between static quarks in SU(2) gauge theory on lattices of volumes
16^4, 32^4, and 48^3*64, with physical extent ranging from 1.3 fm up to 2.7 fm
at beta=2.5, beta=2.635, and beta=2.74. We establish string formation over
physical distances as large as 2 fm. The results are tested against Michael's
sum rules. A detailed investigation of the transverse action and energy flux
tube profiles is provided. As a by-product, we obtain the static lattice
potential in unpreceded accuracy.


title:
An Analysis of Four-quark Energies in SU(2) Lattice Monte Carlo using
  the Flux-tube Symmetry:

abstract:
  Energies of four-quark systems calculated by the static quenched SU(2)
lattice Monte Carlo method are analyzed in $2\times 2$ bases for square,
rectangle, tilted rectangle, linear and quadrilateral geometry configurations
and in $3\times 3$ bases for a non-planar geometry configuration. For small
interquark distances, a lattice effect is taken into account by considering
perimeter dependent terms which are characterized by the cubic symmetry. It is
then found that a parameter $f$ - that can be identified as a gluon field
overlap factor - is rather well described by the form $exp(-[b_sE{\cal
A}+\sqrt{b_s}F{\cal P}])$, where ${\cal A}$ and ${\cal P}$ are the area and
perimeter mainly defined by the positions of the four quarks, $b_s$ is the
string constant in the 2-quark potentials and $E,F$ are constants.


title: Core -- a New Method for Solving Hamiltonian Lattice Systems

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


title: Multigrid Methods for Propagators in Lattice Gauge Theories

abstract:
  Multigrid methods were invented for the solution of discretized partial
differential equations in ordered systems. The slowness of traditional
algorithms is overcome by updates on various length scales. In this article we
discuss generalizations of multigrid methods for disordered systems, in
particular for propagators in lattice gauge theories. A discretized nonabelian
gauge theory can be formulated as a system of statistical mechanics where the
gauge field degrees of freedom are $SU(N)$ matrices on the links of the
lattice. These $SU(N)$ matrices appear as random coefficients in Dirac
equations. We aim at finding an efficient method by which one can solve Dirac
equations without critical slowing down. If this could be achieved, Monte Carlo
simulations of Quantum Chromodynamics (the theory of the strong interaction)
would be accelerated considerably. In principle, however, the methods discussed
can be used in arbitrary space-time dimension and for arbitrary gauge group.
Moreover, there are applications in multigrid Monte Carlo simulations, and for
the definition of block spins and blocked gauge fields in Monte Carlo
renormalization group studies. As a central results it was found that {\em the
geometric multigrid method works in principle in arbitrarily disordered gauge
fields.} Finally, an overview is given of other approaches to the propagator
problem in lattice gauge theories.


title:
Renormalization Group And Scaling Within The Microcanonical Fermionic
  Average Approach

abstract:
  The MFA approach for simulations with dynamical fermions in lattice gauge
theories allows in principle to explore the parameters space of the theory
(e.g. the $\beta, m$ plane for the study of chiral condensate in QED) without
the need of computing the fermionic determinant at each point. We exploit this
possibility for extracting both the renormalization group trajectories
("constant physics lines") and the scaling function, and we test it in the
Schwinger Model. We discuss the applicability of this method to realistic
theories.


title: Exploring Lattice Quantum Chromodynamics by Cooling

abstract:
  The effect of cooling on a number of observables is calculated in SU(2)
lattice gauge theory. The static quark-antiquark potential and spin-dependent
interactions are studied, and the topological charge is monitored. The chiral
symmetry breaking order parameter $\langle \overline{\chi}\chi \rangle$ and
meson correlators are calculated using staggered fermions. Interactions on the
distance scale of a few lattice spacings are found to be essentially eliminated
by cooling, including the spin-dependent potentials. $\langle
\overline{\chi}\chi \rangle$ and meson correlators up to time separations of
several lattice spacings relax very quickly to their free-field values. At
larger times, there is evidence of a difference between the pseudoscalar and
vector channels. A fit to the pseudoscalar correlation function yields ``mass''
values about $2/3$ (in lattice units) of the uncooled masses. These results
raise the question of how to reconcile the large-time behavior of the hadron
correlators with the fact that the spin-dependent potentials and $\langle
\overline{\chi}\chi \rangle$ essentially disappear (in lattice units) after
only a small amount of cooling.


title:
Boundary condition for Staggered Fermion in Lattice Schr\"odinger
  Functional of QCD

abstract:
  The fermionic part of the Schr\"odinger functional of QCD is formulated in
the lattice regularization with the staggered fermion. The boundary condition
imposed on the staggered fermion field are examined in terms of the
four-component Dirac spinor. The boundary terms are different from those of the
Symanzik's theory in the flavor structure due to the species doubling. It is
argued that, in the case of the homogeneous Dirichlet boundary condition,
surface divergence does not occur if the link variables of gauge field are
introduced on the original lattice, not on the blocked one. Its application to
the numerical calculation of the running coupling constant in QCD is discussed.


title: Gribov Noise on the Lattice Axial Current Renormalisation Constant

abstract:
  We study the influence of Gribov copies, in the Landau gauge, on the lattice
renormalisation constant of the axial current, obtained from a Ward identity on
quark state correlation functions, with the Clover action, in quenched SU(3)
gauge theory. A comparison between the gauge invariant determination of the
renorma= lization constant and the gauge dependent one is discussed. We find
that the residual gauge freedom associated to Gribov copies induces observable
effects, which, at the level of numerical accuracy of our simulation, are
included in the statistical uncertainty inherent in a Monte Carlo simulation.
Doubling the statistics suggests that the fluctuation due to the lattice Gribov
ambiguity scales down at least as fast as a pure statistical error.


title:
Domain wall fermions in a waveguide: the phase diagram at large Yukawa
  coupling

abstract:
  In this paper we return to a model with domain wall fermions in a waveguide.
This model contains a Yukawa coupling $y$ which is needed for gauge invariance.
A previous paper left the analysis for large values of this coupling
incomplete. We fill the gap by developing a systematic expansion suitable for
large $y$, and using this, we gain an analytic understanding of the phase
diagram and fermion spectrum. We find that in a sense all the species doublers
come back for large $y$. The conclusion that no lattice chiral gauge theory can
be obtained from this approach therefore remains valid.


title: Generalized Hybrid Monte-Carlo

abstract:
  We propose a modification of the Hybrid Monte-Carlo method to sample
equilibrium distributions of continuous field models. The method allows an
efficient implementation of Fourier acceleration and is shown to reduce
completely critical slowing down for the Gaussian model, i. e., $z=0$.


title:
Low--Temperature Series for Renormalized Operators: the Ferromagnetic
  Square--Lattice Ising Model.

abstract:
  A method for computing low--temperature series for renormalized operators in
the two--dimensional Ising model is proposed. These series are applied to the
study of the properties of the truncated renormalized Hamiltonians when we
start at very low temperature and zero field. The truncated Hamiltonians for
majority rule, Kadanoff transformation and decimation for $2 \times 2$ blocks
depend on the how we approach the first--order phase--transition line. These
Renormalization Group transformations are multi--valued and discontinuous at
this first--order transition line when restricted to some finite--dimensional
interaction space.


title:
Pathological Behavior of Renormalization-Group Maps at High Fields and
  Above the Transition Temperature

abstract:
  We show that decimation transformations applied to high-$q$ Potts models
result in non-Gibbsian measures even for temperatures higher than the
transition temperature. We also show that majority transformations applied to
the Ising model in a very strong field at low temperatures produce non-Gibbsian
measures. This shows that pathological behavior of renormalization-group
transformations is even more widespread than previous examples already
suggested.


title: Simulating the Electroweak Phase Transition in the SU(2) Higgs Model

abstract:
  Numerical simulations are performed to study the finite temperature phase
transition in the SU(2) Higgs model on the lattice. In the presently
investigated range of the Higgs boson mass, below 50 GeV, the phase transition
turns out to be of first order and its strength is rapidly decreasing with
increasing Higgs boson mass. In order to control the systematic errors, we also
perform studies of scaling violations and of finite volume effects.


title: Perfect Lattice Actions for the Gross-Neveu Model at large N

abstract:
  Fixed point actions for free and interacting staggered lattice fermions are
constructed by iterating renormalization group transformations. At large N the
fixed point action for the Gross-Neveu model is a perfect action in the sense
of Hasenfratz and Niedermayer, i.e. cut-off effects are completely eliminated.
In particular, the fermionic 1-particle energy spectrum of the lattice theory
is identical with the one of the continuum even for arbitrarily small
correlation lengths. The cut-off effects of the chiral condensate are
eliminated using a perfect operator. (The paper is stored as a ps-file
containing both the text and 5 figures.)


title: A Solution to the Strong CP Problem

abstract:
  One may argue that QCD solves the strong CP problem by itself, without having
to introduce new symmetries and particles. To test this idea, a lattice
simulation is performed. The problem is investigated in the CP$^3$ model first.
It is found that the model has a first order phase transition in $\theta$ from
a confining phase at small $\theta$ to a deconfining phase at large $\theta$,
and that the critical value of $\theta$ decreases towards zero as $\beta$ is
taken to infinity. This suggests that $\theta$ is tuned to zero in the
continuum limit. Preliminary studies of the SU(2) Yang-Mills theory in four
dimensions show a phase transition in $\theta$ as well, so that it is quite
likely that the strong CP problem in QCD is solved along the same line.


title: Screening of the topological charge in a correlated instanton vacuum

abstract:
  Screening of the topological charge due to he fermion-induced interactions is
an important phenomenon, closely related with the resolution of the strong CP
and U(1) problems. We study the mechanism of such screening in a 'correlated
instanton vacuum', as opposed to the 'random' one. Both scalar and pseudoscalar
gluonic correlators are analyzed by means of an observable that minimizes
finite size effects. Screening of the topological charge is established. This
allows us to calculate the $\eta'$ mass without having to invert the Dirac
operator. We suggest that this method might be used in lattice QCD calculations
as well. Our results for the screening of the topological charge are in
agreement with the chiral Ward identities, and the scalar gluonic correlator
satisfies a low energy theorem first derived by Novikov et al.
\cite{Novikov-etal}. We also propose to evaluate the topological susceptibility
in the Witten-Veneziano formula not in an infinite box in an world $without$
fermions but in an infinitesimal box in a world $with$ fermions.


title:
The Elusive Asymptotic Behavior of the High-Temperature Expansion of the
  Hierarchical Ising Model

abstract:
  We present a differential formulation of the recursion formula of the
hierarchical model which provides a recursive method of calculation for the
high-temperature expansion. We calculate the first 30 coefficients of the high
temperature expansion of the magnetic susceptibility of the Ising hierarchical
model with 12 significant digits. We study the departure from the approximation
which consists of identifying the coefficients with the values they would take
if a $[0,1]$ Pad\'e approximant were exact. We show that, when the order in the
high-temperature expansion increases, the departure from this approximation
grows more slowly than for nearest neighbor models. As a consequence, the value
of the critical exponent $\gamma $ estimated using Pad\'e approximants
converges very slowly and the estimations using 30 coefficients have errors
larger than 0.05. A (presumably much) larger number of coefficients is
necessary to obtain the critical exponents with a precision comparable to the
precision obtained for nearest neighbor models with less coefficients. We also
discuss the possibility of constructing models where a $[0,1]$ Pad\'e
approximant would be exact.


title:
Lattice $(\Phi^4)_4$ Effective Potential Giving Spontaneous Symmetry
  Breaking and the Role of the Higgs Mass

abstract:
  We present a critical reappraisal of the available results on the broken
phase of $\lambda(\Phi^4)_4$ theory, as obtained from rigorous formal analyses
and from lattice calculations. All the existing evidence is compatible with
Spontaneous Symmetry Breaking but dictates a trivially free shifted field that
becomes controlled by a quadratic hamiltonian in the continuum limit. As
recently pointed out, this implies that the simple one-loop effective potential
should become effectively exact. Moreover, the usual naive assumption that the
Higgs mass-squared $m^2_h$ is proportional to its ``renormalized''
self-coupling $\lambda_R$ is not valid outside perturbation theory: the
appropriate continuum limit has $m_h$ finite and vanishing $\lambda_R$. A Monte
Carlo lattice computation of the $\lambda(\Phi^4)_4$ effective potential, both
in the single-component and in the O(2)-symmetric cases, is shown to agree very
well with the one-loop prediction. Moreover, its perturbative leading-log
improvement (based on the concept of $\lambda_R$) fails to reproduce the Monte
Carlo data. These results, while supporting in a new fashion the peculiar
``triviality'' of the $\lambda(\Phi^4)_4$ theory, also imply that, outside
perturbation theory, the magnitude of the Higgs mass does not give a measure of
the observable interactions in the scalar sector of the standard model.


title: Confining Forces and String Formation from the Lattice

abstract:
  We show the running coupling as derived from the SU(3) QQ potential and
discuss preliminary results on spin dependent heavy quark potentials from high
statistics lattice simulations of SU(2) gauge theory. The precision suffices to
study scaling properties and lattice artifacts (at short distances). We
identify the Coulomb like short range interaction as a mixed vector-scalar
exchange. We measure flux tube formation between a static QQ pair over physical
distances up to 2 fm, with a spatial resolution as small as .05 fm. Consistency
with the string picture is found for separation larger than about 1 fm, with a
half width of the profile of approximately .7 fm.


title:
Real Space Renormalization Group Analysis of U(1)-Gauge Theory with
  theta-term in 2 Dimensions

abstract:
  U(1) lattice gauge theory with $\theta$-term is investigated by real space
renormalization group approach. Flows of renormalized coupling constants are
analyzed. For each $\theta$, renormalization flows converge to a single
trajectory irrespective of bare coupling constants of real action. For $\theta
\not= \pi$ the system is in the confinement phase controlled by an infrared
fixed point. We found a phase transition at $\theta = \pi$. Imaginary part of
the action given by $\theta$-term stays fixed under renormalization group
transformations leading to deconfinement.


title:
Universality and the Deconfinement Phase Transition in SU(2) Lattice
  Gauge Theory

abstract:
  We study the three dimensional fundamental-adjoint $SU(2)$ lattice gauge
theory at non-zero temperatures by Monte Carlo simulations. On an $8^3 \times
2$ lattice, at $\beta_A = 1.1$, where $\beta_A$ is the adjoint coupling, we
find no evidence of any transition at the location of a previously known bulk
phase transition around $\beta = 1.33$. Moreover, the deconfinement transition
at $ \beta_A = 1.1$ occurs at $\beta=1.20$ and is of first order for $\beta_A
\ge 1.1$, thus implying a change of universality class from that of the Wilson
action at $\beta_A=0$. Computations of the plaquette susceptibility and the
temporal and spatial Polyakov loops on $8^3 \times 4$ and $16^3 \times 8$
lattices at $\beta_A = 1.1$ further support these conclusions and suggest that
the previously claimed bulk transition around $\beta = 1.33$ is, in fact, the
first order deconfinement transition. Simulations at larger $\beta_A$ and the
measurements of the mass gaps from the correlation functions of temporal and
spatial Polyakov loops also confirm the temperature dependent nature of the
above transition. The consequences of our results on universality are
discussed.


title: Low-Temperature Series Expansions for the Spin-1 Ising Model

abstract:
  The finite lattice method of series expansion has been used to extend
low-temperature series for the partition function, order parameter and
susceptibility of the spin-1 Ising model on the square lattice. A new formalism
is described that uses two distinct transfer matrix approaches in order to
significantly reduce computer memory requirements and which permits the
derivation of the series to 79th order. Subsequent analysis of the series
clearly confirms that the spin-1 model has the same dominant critical exponents
as the spin-$\frac{1}{2}$ Ising model. Accurate estimates for both the critical
temperature and non-physical singularities are obtained. In addition, evidence
for a non-analytic confluent correction with exponent $\Delta_{1} = 1.1 \pm
0.1$ is found.


title:
Spectrum of the Dirac Operator and Inversion Algorithms with Dynamical
  Staggered Fermions

abstract:
  Complete spectra of the staggered Dirac operator $\Dirac$ are determined in
four-dimensional $SU(2)$ gauge fields with and without dynamical fermions.
  An attempt is made to relate the performance of multigrid and conjugate
gradient algorithms for propagators with the distribution of the eigenvalues
of~$\Dirac$.


title: Lattice Results for Heavy Light Matrix Elements

abstract:
  Lattice results for heavy light matrix elements are reviewed and some of
their implications are very briefly discussed. Despite the fact that in most
cases the lattice results for weak matrix elements at the moment have only a
modest accuracy of about 20--30\% they already have important phenomenological
repercussions; e.g.\ for $V_{td}/V_{ts}$, $x_s/x_d$ and $B\to K^\ast\gamma$.
Presented at the XXVII International Conference on High Energy Physics,
Glasgow, July 1994.


title: Chiral symmetry and lattice gauge theory

abstract:
  I review the problem of formulating chiral symmetry in lattice gauge theory.
I discuss recent approaches involving an infinite tower of additional heavy
states to absorb Fermion doublers. For hadronic physics this provides a natural
scheme for taking quark masses to zero without requiring a precise tuning of
parameters. A mirror Fermion variation provides a possible way of extending the
picture to chirally coupled light Fermions. Talk presented at "Quark
Confinement and the Hadron Spectrum," Como, Italy, 20-24 June 1994.


title: Tricritical Behavior of Two-Dimensional Scalar Field Theories

abstract:
  We compute by Monte Carlo numerical simulations the critical exponents of
two-dimensional scalar field theories at the $\lambda\phi^6$ tricritical point.
The results are in agreement with the Zamolodchikov conjecture based on
conformal invariance.


title:
Monte Carlo calculation for systems consisting of several coordinate
  patches

abstract:
  I investigate the time step dependence of Monte Carlo simulations for
coordinate-spaces consisting of several patches. It is shown that a naive
kinetic term does not necessarily converge to the same spectrum as a
Hamiltonian calculation. Then an improved kinetic term is presented which
allows one to connect the Monte Carlo and Rayleigh-Ritz results of intermediate
volume SU(2) gauge theory.


title: The Gluon Propagator on a Large Volume, at $\beta=6.0$

abstract:
  We present the results of a high statistics lattice study of the gluon
propagator, in the Landau gauge, at $\beta=6.0$. As suggested by previous
studies, we find that, in momentum space, the propagator is well described by
the expression $G(k^2)= \Big[ M^2 + Z\cdot k^2(k^2/\Lambda^2)^\eta\Big]^{-1} $.
By comparing $G(k^2)$ on different volumes, we obtain a precise determination
of the exponent $\eta=0.532(12)$, and verify that $M^2$ does not vanish in the
infinite volume limit. The behaviour of $\eta$ and $M^2$ in the continuum limit
is not known, and can only be studied by increasing the value of $\beta$.


title: An ``Improved" Lattice Study of Semi-leptonic Decays of D-Mesons

abstract:
  We present results of a lattice computation of the matrix elements of the
vector and axial-vector currents which are relevant for the semi-leptonic
decays $D \rightarrow K$ and $D \rightarrow K^*$. The computations are
performed in the quenched approximation to lattice QCD on a $24^3 \times 48$
lattice at $\beta=6.2$, using an $O(a)$-improved fermionic action. In the limit
of zero lepton masses the semi-leptonic decays $D \rightarrow K$ and $D
\rightarrow K^*$ are described by four form factors: $f^{+}_K,V,A_1$ and $A_2$,
which are functions of $q^2$, where $q^{\mu}$ is the four-momentum transferred
in the process. Our results for these form factors at $q^2=0$ are:
$f^+_K(0)=0.67 \er{7}{8}$ , $V(0)=1.01 \err{30}{13}$ , $A_1(0)=0.70
\err{7}{10}$ , $A_2(0)=0.66 \err{10}{15}$ , which are consistent with the most
recent experimental world average values. We have also determined the $q^2$
dependence of the form factors, which we find to be reasonably well described
by a simple pole-dominance model. Results for other form factors, including
those relevant to the decays \dpi and \drho, are also given.


title:
Geometrical Volume Effects in the Computation of the Slope of the
  Isgur-Wise Function

abstract:
  We use a method recently suggested for evaluating the slope of the Isgur-Wise
function, at the zero-recoil point, on the lattice. The computations are
performed in the quenched approximation to lattice QCD, on a $24^3 \times 48$
lattice at $\beta=6.2$, using an $O(a)$-improved action for the fermions. We
have found unexpectedly large finite-volume effects in such a calculation.
These volume corrections turned out to be purely geometrical and independent of
the dynamics of the system. After the study of these effects on a smaller
volume and for different quark masses, we give approximate expressions that
account for them. Using these approximations we find $\xi^\prime(1)=-1.7 \pm
0.2$ and $\xi^\prime(1)=-1.4 +0.2-0.1$ for the slope of the Isgur-Wise
function, for two mesons composed of a heavy quark slightly heavier and
lighter, respectively, than the charm quark, and in both cases, a light
antiquark whose mass is about that of the strange quark.


title:
The beta function and equation of state for QCD with two flavors of
  quarks

abstract:
  We measure the pressure and energy density of two flavor QCD in a wide range
of quark masses and temperatures. The pressure is obtained from an integral
over the average plaquette or psi-bar-psi. We measure the QCD beta function,
including the anomalous dimension of the quark mass, in new Monte Carlo
simulations and from results in the literature. We use it to find the
interaction measure, E-3p, yielding non-perturbative values for both the energy
density E and the pressure p. uuencoded compressed PostScript file Revised
version should work on more PostScript printers.


title:
Embedding the N=2 Supersymmetric Yang-Mills Theory in the Adjoint
  Higgs-Yukawa Model on the Lattice

abstract:
  The N=2 supersymmetric Yang-Mills theory is formulated on the lattice. The
feasibility of numerical simulations is discussed.


title:
The continuum limit of $f_B$ from the lattice in the static
  approximation

abstract:
  We present an analysis of the continuum extrapolation of $f_B$ in the static
approximation from lattice data. The method described here aims to uncover the
systematic effects which enter in this extrapolation and has not been described
before. Our conclusions are that we see statistical evidence for scaling of
$f_B^{stat}$ for inverse lattice spacings $\gtap 2$ GeV but not for $\ltap 2$
GeV. We observe a lack of {\em asymptotic} scaling for a variety of quantities,
including $f_B^{stat}$, at all energy scales considered. This can be associated
with finite lattice spacing systematics. Once these effects are taken into
account, we obtain a value of 230(35) MeV for $f_B^{stat}$ in the continuum
where the error represents uncertainties due to both the statistics and the
continuum extrapolation. In this method there is no error due to uncertainties
in the renormalization constant connecting the lattice and continuum effective
theories.


title: QCD Strings as Constrained Grassmannian Sigma Model:

abstract:
  We present calculations for the effective action of string world sheet in R3
and R4 utilizing its correspondence with the constrained Grassmannian sigma
model. Minimal surfaces describe the dynamics of open strings while harmonic
surfaces describe that of closed strings. The one-loop effective action for
these are calculated with instanton and anti-instanton background, reprsenting
N-string interactions at the tree level. The effective action is found to be
the partition function of a classical modified Coulomb gas in the confining
phase, with a dynamically generated mass gap.


title: Domain Wall Fermions and Chiral Gauge Theories

abstract:
  We review the status of the domain wall fermion approach to construct chiral
gauge theories on the lattice. In this model an extra, fifth dimension is added
and our 4-dimensional world lives on a domainwall induced by a soliton shaped
mass defect that depends on the extra dimension only. We demonstrate that the
domain wall model gives the correct anomaly structure when external gauge
fields are used. We discuss two ways of adding dynamical gauge fields aiming at
a lattice regularized chiral gauge theory. An approach is presented to keep the
lattice infinite by regarding the fifth direction as the time-axis of a
4-dimensional Hamiltonian. Finally, a prospect to use domain wall fermions for
simulating QCD is given.


title:
Correlation Function at $\beta_t$ in the Disordered Phase of 2D Potts
  Models

abstract:
  We use Monte Carlo simulations to measure the spin-spin correlation function
in the disordered phase of two-dimensional $q$-state Potts models with
$q=10,15$, and $20$ at the first-order transition point $\beta_t$. To extract
the correlation length $\xi_d$ from the exponential decay of the correlation
function over several decades with the desired accuracy we make extensively use
of cluster-update techniques and improved estimators. Our results for $\xi_d$
are compatible with an analytic formula. As a byproduct we also measure the
energy moments in the disordered phase and find very good agreement with a
recent large $q$ expansion at $\beta_t$.


title: Random Walk Model on a Hyper-Spherical Lattice

abstract:
  We use a one-dimensional random walk on $D$-dimensional hyper-spheres to
determine the critical behavior of statistical systems in hyper-spherical
geometries. First, we demonstrate the properties of such walk by studying the
phase diagram of a percolation problem. We find a line of second and first
order phase transitions separated by a tricritical point. Then, we analyze the
adsorption-desorption transition for a polymer growing near the attractive
boundary of a cylindrical cell membrane. We find that the fraction of adsorbed
monomers on the boundary vanishes exponentially when the adsorption energy
decreases towards its critical value. We observe a crossover phenomenon to an
area of linear growth at energies of the order of the inverse cell radius.


title:
Recent Developments in Monte Carlo Simulations of First-Order Phase
  Transitions

abstract:
  In the past few years considerable progress has been made in Monte Carlo
simulations of first-order phase transitions and in the analysis of the
resulting finite-size data. In this paper special emphasis will be placed on
multicanonical simulations using multigrid update techniques, on numerical
estimates of interface tensions, and on accurate methods for determining the
transition point and latent heat.


title:
Quantum Behaviour of the Flux Tube: A comparison between QFT predictions
  and lattice gauge theory simulations

abstract:
  We review some universal features of the colour flux tube of gauge theories
in the confining phase predicted by the infrared conformal limit of the
underlying string theory. In particular we discuss shape effects in Wilson
loops and rederive in a general way the logarithmic growth of the mean square
width of the flux tube as a function of the interquark separation. Recent data
on three-dimensional Z_2 gauge theory, combined with high precision data on the
interface physics of the 3D Ising model fit nicely to this behaviour over a
range of more than two orders of magnitude


title: Polymer-Chain Adsorption Transition at a Cylindrical Boundary

abstract:
  In a recent letter, a simple method was proposed to generate solvable models
that predict the critical properties of statistical systems in hyperspherical
geometries. To that end, it was shown how to reduce a random walk in $D$
dimensions to an anisotropic one-dimensional random walk on concentric
hyperspheres. Here, I construct such a random walk to model the
adsorption-desorption transition of polymer chains growing near an attractive
cylindrical boundary such as that of a cell membrane. I find that the fraction
of adsorbed monomers on the boundary vanishes exponentially when the adsorption
energy decreases towards its critical value. When the adsorption energy rises
beyond a certain value above the critical point whose scale is set by the
radius of the cell, the adsorption fraction exhibits a crossover to a linear
increase characteristic to polymers growing near planar boundaries.


title: Composite Weak Bosons: a Lattice Analysis

abstract:
  We present a lattice analysis of a confining Yang-Mills theory without
Goldstone boson. We have analytically investigated the model by a strong
coupling expansion and by an intensive lattice Monte Carlo simulation using
standard lattice QCD methods. We show that this theory is an interesting
candidate for describing weak bosons as composite particles.


title: Composite Weak Bosons: a Lattice Monte Carlo Analysis

abstract:
  We present a lattice Monte Carlo simulation for the evaluation of the
spectrum of a confining Yang-Mills theory without Goldstone boson. We show that
this theory is a very good candidate for describing composite weak bosons. In
order to perform the spectrum analysis we have used standard lattice QCD Monte
Carlo methods. We have also developed an efficient method to evaluate the mass
of the pseudoscalar isosinglet which is present in our theory.


title:
Composite Weak Bosons in a Confining Gauge Theory without Goldstone
  Bosons: a Strong Coupling Expansion Analysis

abstract:
  We consider a confining Yang-Mills theory without Goldstone Bosons which
could describe the bosonic sector of the weak interactions. This model can be
gauge invariantly regularized on a lattice. A strong coupling analysis of the
low lying bound state spectrum indicates that the vector isotriplet bound state
(the right quantum number to represent the W-boson) could be the lightest state
if the mass of the pseudoscalar isosinglet is raised sufficiently by the effect
of the chiral anomaly (in analogy to the $\eta'$ mechanism of QCD). This work
is a preliminary study in support to an intensive lattice Monte Carlo analysis
of the model.


title: SU(3) Lattice Gauge Theory With Adjoint Action At Nonzero Temperature

abstract:
  We study the thermal phase diagram of pure SU(3) gauge theory with
fundamental and adjoint couplings. We improve previous estimates of the
position of the bulk transition line and determine the thermal deconfinement
transition lines for $N_t=2,4,6,$ and 8. For $N_t > 4$ the deconfinement
transition line splits cleanly away from the bulk transition line. With
increasing $N_t$ the thermal deconfinement transition lines shift to
increasingly weaker coupling, joining onto the bulk transition line at
increasingly larger $\beta_a$ in a pattern consistent with the usual
universality picture of lattice gauge theories.


title: Chiral Perturbation Theory and the Quenched Approximation of QCD

abstract:
  The quenched approximation for QCD is, at present and in the foreseeable
future, unavoidable in lattice calculations with realistic choices of the
lattice spacing, volume and quark masses. In these lectures, I review the
analytic study of the effects of quenching based on chiral perturbation theory.
Quenched chiral perturbation theory leads to quantitative insight into the
difference between quenched and unquenched QCD, and reveals clearly diseases
which plague quenched QCD. A short review of the ideas underlying chiral
perturbation theory is included.


title: Flux tubes and topological charges in finite-temperature lattice QCD

abstract:
  Topological properties of the vacuum were investigated in finite-temperature
lattice QCD without and with dynamical quarks using a local operator of
topological charge density and a variant of cooling. Below the deconfinement
temperature evidence for flux tube formation was observed in the distribution
of topological charge density around a static $Q\bar Q$ pair. With dynamical
quarks, the flux tube breaks when the distance between the static quark and
antiquark increases.


title:
An Analytic Study of the Phase Structure of Lattice QCD with Wilson
  Fermions at Infinitely Strong Coupling

abstract:
  The phase structure of lattice QCD with two flavors and Wilson fermions is
studied analytically. At $\beta=0$ we obtain rigorous lower and upper bounds
for the critical hopping parameter $k_c(0)$ from a convergent hopping parameter
expansion to infinite order. The result supports the value $k_c(0)=\frac{1}{4}$
observed in Monte Carlo simulations.


title: Computational Ergodicity of $s^4$

abstract:
  It is known that there are four-manifolds which are not algorithmically
recognizable. This implies that there exist triangulations of these manifolds
which are separated by large barriers from the point of view of the computer
algorithm. We have not observed these barriers for triangulations of $S^4$.


title:
Asymptotic Scaling in the Two-Dimensional $O(3)$ $\sigma$-Model at
  Correlation Length $10^5$

abstract:
  We carry out a high-precision Monte Carlo simulation of the two-dimensional
$O(3)$-invariant $\sigma$-model at correlation lengths $\xi$ up to $\sim 10^5$.
Our work employs a new and powerful method for extrapolating finite-volume
Monte Carlo data to infinite volume, based on finite-size-scaling theory. We
discuss carefully the systematic and statistical errors in this extrapolation.
We then compare the extrapolated data to the renormalization-group predictions.
The deviation from asymptotic scaling, which is $\approx 25\%$ at $\xi \sim
10^2$, decreases to $\approx 4\%$ at $\xi \sim 10^5$.


title:
A General Method for Non-Perturbative Renormalization of Lattice
  Operators

abstract:
  We propose a non-perturbative method for computing the renormalization
constants of generic composite operators. This method is intended to reduce
some systematic errors, which are present when one tries to obtain physical
predictions from the matrix elements of lattice operators. We also present the
results of a calculation of the renormalization constants of several
two-fermion operators, obtained, with our method, by numerical simulation of
$QCD$, on a $16^3 \times 32$ lattice, at $\beta=6.0$. The results of this
simulation are encouraging, and further applications to four-fermion operators
and to the heavy quark effective theory are proposed.


title:
Lattice Calculation of D- and B-meson Semileptonic Decays, using the
  Clover Action at beta=6.0 on APE

abstract:
  We present the results of a high statistics lattice calculation of hadronic
form factors relevant for $D-$ and $B-$meson semi-leptonic decays into light
pseudoscalar and vector mesons. The results have been obtained by averaging
over 170 gauge field configurations, generated in the quenched approximation,
at $\beta=6.0$, on a $18^3 \times 64$ lattice, using the $O(a)$-improved
SW-Clover action.From the study of the matrix element $<K^-\vert J_\mu \vert
D^0>$, we obtain $f_+ (0)=0.78\pm 0.08$ and from the matrix element $<\bar K^{*
0}\vert J_\mu \vert D^+>$ we obtain $V(0)=1.08\pm 0.22$, $A_1(0)=0.67\pm 0.11$
and $A_2(0)=0.49\pm 0.34$. We also obtain the ratios $V(0)/A_1(0)=1.6\pm 0.3$
and $A_2(0)/A_1(0)= 0.7\pm 0.4$. Our predictions for the different form factors
are in good agreement with the experimental data, although, in the case of
$A_2(0)$, the errors are still too large to draw any firm conclusion. With the
help of the Heavy Quark Effective Theory (HQET) we have also extrapolated the
lattice results to $B$-meson decays. The form factors follow a behaviour
compatible with the HQET predictions. Our results are in agreement with a
previous lattice calculation, performed at $\beta=6.4$, using the standard
Wilson action.


title: Chiral invariance and lattice fermions with minimal doubling

abstract:
  A few years ago some attention has been given to a fermionic action on the
lattice, with a Wilson-like term which is chirally invariant but breaks the
hypercubic space-time lattice symmetry. This action describes two Dirac fields
in the continuum limit, provided the coefficient $\lambda$ of the Wilson-like
term satisfies $\lambda > \frac{1}{2}$. In this letter it is shown that for
$\frac{1}{2} < \lambda \leq 1$ the theory is link-reflection positive. The
propagator has the expected real energy poles. Modulo a phase shift on the
fermions, the only relevant terms which can be added to the action respecting
its symmetries have dimension $4$.


title: Efficient Hadronic Operators in Lattice Gauge Theory

abstract:
  We propose the study of non-local gauge invariant operators to obtain an
uncontaminated ground state for hadrons. The efficiency of the operators is
shown by looking at the wave function of the first excited state, which has a
node as a function of spatial extent of the operator.


title: Continuum limit of field theories regularized on a random lattice

abstract:
  The continuum limit and scaling properties of an asymptotically free field
theory regularized on a random lattice are compared with those on a regular
square lattice. We work on random lattices parametrized by a degree of
``randomness'' $\kappa$. We show that the continuum limit exists and different
$\kappa$ are related by a finite renormalization.


title: Instanton size distributions from calibrated cooling

abstract:
  Using an under-relaxed cooling algorithm we investigated the vacuum in the
$2d\ O(3)$ model and $4d$ pure gauge $SU(2)$. We calibrated the amount of
cooling performed to have similar physical effect at different lattice
spacings.


title: A new simulation algorithm for lattice QCD with dynamical quarks

abstract:
  A previously introduced multi-boson technique for the simulation of QCD with
dynamical quarks is described and some results of first test runs on a
$6^3\times12$ lattice with Wilson quarks and gauge group SU(2) are reported.


title:
Universality and the approach to the continuum limit in lattice gauge
  theory

abstract:
  The universality of the continuum limit and the applicability of renormalized
perturbation theory are tested in the SU(2) lattice gauge theory by computing
two different non-perturbatively defined running couplings over a large range
of energies. The lattice data (which were generated on the powerful APE
computers at Rome II and DESY) are extrapolated to the continuum limit by
simulating sequences of lattices with decreasing spacings. Our results confirm
the expected universality at all energies to a precision of a few percent. We
find, however, that perturbation theory must be used with care when matching
different renormalized couplings at high energies.


title: Two-loop computation of a finite volume running coupling on the lattice

abstract:
  In pure SU(2) gauge theory we compute the two-loop coefficient in the
relation between the lattice bare coupling and the running coupling defined
through the Schroedinger functional. This result is required to relate the
latter to the MSbar-coupling in our programme to compute alpha_s. In addition
it allows us to implement O(a) improvement of the Schroedinger functional to
two-loop order. The two-loop beta-function is verified in a perturbative
computation on the lattice, and the behavior of expansions in the standard and
in the Parisi-improved bare couplings are investigated beyond one loop.


title:
Exact solution (by algebraic methods) of the lattice Schwinger model in
  the strong-coupling regime

abstract:
  Using the monomer--dimer representation of the lattice Schwinger model, with
$N_f =1$ Wilson fermions in the strong--coupling regime ($\beta=0$), we
evaluate its partition function, $Z$, exactly on finite lattices. By studying
the zeroes of $Z(k)$ in the complex plane $(Re(k),Im(k))$ for a large number of
small lattices, we find the zeroes closest to the real axis for infinite
stripes in temporal direction and spatial extent $S=2$ and 3. We find evidence
for the existence of a critical value for the hopping parameter in the
thermodynamic limit $S\rightarrow \infty$ on the real axis at about $k_c \simeq
0.39$. By looking at the behaviour of quantities, such as the chiral
condensate, the chiral susceptibility and the third derivative of $Z$ with
respect to $1/2k$, close to the critical point $k_c$, we find some indications
for a continuous phase transition.


title:
Three-Dimensional SU(3) gauge theory and the Spatial String Tension of
  the (3+1)-Dimensional Finite Temperature SU(3) Gauge Theory

abstract:
  We establish a close relation between the spatial string tension of the
(3+1)-dimensional $SU(3)$ gauge theory at finite temperature ($\sigma_s$) and
the string tension of the 3-dimensional $SU(3)$ gauge theory ($\sigma_3$) which
is similar to what has been found previously for $SU(2)$. We obtain
$\sqrt{\sigma_3} = (0.554 \pm 0.004) g_3^2$ and $\sqrt{\sigma_s} = (0.586 \pm
0.045)g^2(T) T$, respectively. For temperatures larger than twice the critical
temperature results are consistent with a temperature dependent coupling
running according to the two-loop $\beta$-function with $\Lambda_T =
0.118(36)T_c$.


title: Hadron Properties in the Vicinity of $T_c$

abstract:
  Modifications of hadron masses and some of their basic properties with
temperature or nuclear density are considered as one possible signature for the
formation of dense hadronic matter in nuclear collisions. We discuss here some
basic results on the temperature dependence of hadron properties obtained from
calculations of hadron correlation functions, the chiral condensate as well as
the equation of state in finite temperature lattice QCD.


title: Hadron correlators with improved fermions

abstract:
  We investigate point-to-point correlation functions for various mesonic and
baryonic channels using the ${\cal O}(a)$-improved Wilson action due to
Sheikholeslami and Wohlert. We consider propagators to both time slices 0 and
1. We find that discretisation effects are more pronounced than those reported
with unimproved Wilson fermions, but that the same procedure for removing
finite size effects is successful. Extrapolating to the chiral limit, we see
the notable features predicted phenomenologically: the ratio of interacting to
free correlators in the vector channel is roughly constant to about 1 fm, while
in the pseudoscalar channel the ratio increases markedly due to the strong
binding.


title:
Complex-Temperature Singularities in the $d=2$ Ising Model. II.
  Triangular Lattice

abstract:
  We investigate complex-temperature singularities in the Ising model on the
triangular lattice. Extending an earlier analysis of the low-temperature series
expansions for the (zero-field) susceptibility $\bar\chi$ by Guttmann
\cite{g75} to include the use of differential approximants, we obtain further
evidence in support of his conclusion that the exponent describing the
divergence in $\chi$ at $u=u_e=-1/3$ (where $u = e^{-4K}$) is $\gamma_e'=5/4$
and refine his estimate of the critical amplitude. We discuss the remarkable
nature of this singularity, at which the spontaneous magnetisation diverges
(with exponent $\beta_e=-1/8$) and show that it lies at the endpoint of a
singular line segment constituting part of the natural boundaries of the free
energy in the complex $u$ plane. Using exact results, we find that the specific
heat has a divergent singularity at $u=-1/3$ with exponent $\alpha_e'=1$, so
that the relation $\alpha_e'+2\beta_e+\gamma_e'=2$ is satisfied. We also study
the singularity at $u=u_s=-1$, where $M$ vanishes (with $\beta_s=3/8$) and $C$
diverges logarithmically (with $\alpha_s' = \alpha_s = 0$).


title: Leptonic Decays of $B$- and $D$-Mesons

abstract:
  The present status of lattice calculations of $f_D$, $f_B$ and some mass
splittings are discussed. When one includes the uncertainties due to
discretization errors, the results do not yet have a sufficient precision to be
relevant to phenomenological applications. There are, however, good prospects
of cutting down the uncertainties by a factor of 2 or more soon.


title: Do Wilson Fermions Induce an Adjoint Gauge Coupling?

abstract:
  Expansions of the Wilson determinant in lattice QCD with quarks produce gauge
action terms which shift the coupling constant of the fundamental
representation plaquette action and induce an adjoint representation plaquette
action. We study the magnitude of these induced couplings with two flavors of
Wilson fermions. We utilize a microcanonical demon method, which allows us to
measure the induced couplings directly from gauge configurations generated by
full fermionic simulations.


title: Three-dimensional $x-y$ model with the Chern-Simons term

abstract:
  We investigate the influence of the Chern-Simons term coupled to the
three-dimensional $x-y$ model. This term endows vortices with an internal
angular momentum and thus gives them arbitrary statistics. The Chern-Simons
term for the $x-y$ model takes an integer value which can be written as a sum
over all vortex lines of the product of the vortex charge and the winding
number of the internal phase angle along that vortex line. We have used the
Monte-Carlo method to study the three-dimensional $x-y$ model with the
Chern-Simons term. Our findings suggest that this model belongs to the $x-y$
universality class with the critical temperature growing with increasing
internal angular momentum.


title: Logarithmic Corrections to Scaling in the $XY_2$--Model

abstract:
  We study the distribution of partition function zeroes for the $XY$--model in
two dimensions. In particular we find the scaling behaviour of the end of the
distribution of zeroes in the complex external magnetic field plane in the
thermodynamic limit (the Yang--Lee edge) and the form for the density of these
zeroes. Assuming that finite--size scaling holds, we show that there have to
exist logarithmic corrections to the leading scaling behaviour of thermodynamic
quantities in this model. These logarithmic corrections are also manifest in
the finite--size scaling formulae and we identify them numerically. The method
presented here can be used to check the compatibility of scaling behaviour of
odd and even thermodynamic functions in other models too.


title:
Topological charge density around static colour sources in lattice QCD
  with dynamical quarks

abstract:
  We update our numerical investigation of topological structures around static
quarks in pure gauge QCD by results of the first runs including dynamical
quarks. Simulations were performed on an $8^3\times4$ lattice, with $SU(3)$
Wilson action, with 3 flavours of quarks of equal mass, both in the confinement
and deconfinement phase. In the confinement phase we observe indications for
the existence of a flux tube between a static quark and antiquark, flux-tube
breaking for large separations, and local correlation between the topological
charge density and chiral condensate. In the deconfinement phase almost all
configurations turn out to be topologically trivial.


title: Systematic Expansion for Full QCD Based on the Valence Approximation

abstract:
  We construct a systematic expansion for full QCD. The leading term gives the
valence (quenched) approximation.


title: Expansion Aspect of Color Transparency on the Lattice

abstract:
  The opportunity to observe color transparency (CT) is determined by how
rapidly a small-sized hadronic wave packet expands. Here we use SU(2) lattice
gauge theory with Wilson fermions in the quenched approximation to investigate
the expansion. The wave packet is modeled by a point hadronic source, often
used as an interpolating field in lattice calculations. The procedure is to
determine the Euclidean time (t), pion channel, Bethe-Salpeter amplitude
$\Psi(r,t)$, and then evaluate $b^2(t)=\int d^3 r \Psi(r,t) r^2 sin^2 \theta
\Psi_{\pi}(r)$. This quantity represents the soft interaction of a small-sized
wave packet with a pion. The time dependence of $b^2(t)$ is fit as a
superposition of three states, which is found sufficient to reproduce a reduced
size wave packet. Using this superposition allows us to make the analytic
continuation required to study the wave packet expansion in real time. We find
that the matrix elements of the soft interaction $\hat b^2$ between the excited
and ground state decrease rapidly with the energy of the excited state.


title: Construction of staples in lattice gauge theory on a parallel computer

abstract:
  We propose a simple method to construct staples in lattice gauge theory with
Wilson action on a parallel computer. This method can be applicable to any
dimensional system and to any dimensional division without difficulty.
Furthermore this requires rather small working area to realize gauge simulation
on a parallel computer.


title: Dynamical Triangulation with Fluctuating Topology

abstract:
  We consider a dynamical triangulation model of euclidean quantum gravity
where the topology is not fixed. This model is equivalent to a tensor
generalization of the matrix model of two dimensional quantum gravity. A set of
moves is given that allows Monte Carlo simulation of this model. Some
preliminary results are presented for the case of four dimensions.


title: Chiral symmetry on the lattice

abstract:
  I review some of the difficulties associated with chiral symmetry in the
context of a lattice regulator. I discuss the structure of Wilson Fermions when
the hopping parameter is in the vicinity of its critical value. Here one flavor
contrasts sharply with the case of more, where a residual chiral symmetry
survives anomalies. I briefly discuss the surface mode approach, the use of
mirror Fermions to cancel anomalies, and finally speculate on the problems with
lattice versions of the standard model.


title: New critical phenomena in 2d quantum gravity

abstract:
  We study $q=10$ and $q=200$ state Potts models on dynamical triangulated
lattices and demonstrate that these models exhibit continuous phase
transitions, contrary to the first order transition present on regular
lattices. For $q=10$ the transition seems to be of 2nd order, while it seems to
be of 3rd order for $q=200$. For $q=200$ the phase transition also induces a
transition between typical fractal structures of the piecewise linear surfaces
corresponding to the triangulations. The typical surface changes from having a
tree-like structure to a fractal structure characterizing pure gravity when the
temperature drops below the critical temperature. An investigation of the
alignment of spin clusters shows that they are strongly correlated to the
underlying fractal structure of the triangulated surfaces.


title:
Universal behaviour of the SU(2) running coupling constant in the
  continuum limit

abstract:
  We present data from the ALPHA Collaboration about lattice calculation of
SU(2) pure--gauge running coupling constant, obtained with two different
definitions of the coupling itself, which show universality of the continuum
limit and clarify the applicability of renormalized perturbation theory.


title: Deconfinement transition and monopoles in $T\neq0$ $SU(2)$ QCD

abstract:
  The role of monopoles in the deconfinement transition is discussed in the
framework of abelian projection in the maximally abelian gauge in $T\neq0$
$SU(2)$ QCD. Only one (or a few near $\beta_c$) long connected monopole loop
exists uniformly through the whole lattice in each vacuum configuration in
addition to some very short loops in the confinement phase and the long loop
disappears in the deep deconfinement region. Energy-entropy balance of the long
loops of maximally extended monopoles explains the existence of the
deconfinement transition and reproduces roughly the value of the critical
temperature.


title: Hierarchical renormalization goup fixed points

abstract:
  Hierarchical renormalization group transformations are related to
non-associative algebras. Non-trivial infrared fixed points are shown to be
solutions of polynomial equations. At the example of a scalar model in
$d(\ge2)$ dimensions some methods for the solution of these algebraic equations
are presented.


title: Flavor-Parity Breaking in the NJL Model with Wilson Fermions

abstract:
  The Nambu--Jona-Lasinio model is chirally symmetric. Addition of a Wilson
term explicitly breaks this symmetry and leaves the model with a remaining
parity-flavor symmetry. In the approximation of a large number of colors it has
been shown that there is a phase where the remaining parity-flavor symmetry is
spontaneously broken and that on the phase boundary all pions become massless.
Using numerical simulations we confirm the existence of this phase for the case
of two flavors and two colors. We also confirm the large N prediction of the
existence of large finite size effects that alter the shape of the phase
boundary dramatically when periodic boundary conditions are used.


title: Perfect Lattice Actions for the Gross-Neveu Model

abstract:
  We apply the method of Hasenfratz and Niedermayer to analytically construct
perfect lattice actions for the Gross--Neveu model. In the large $N$ limit
these actions display an exactly perfect scaling, i.e. cut-off artifacts are
completely eliminated even at arbitrarily short correlation length. Also the
energy spectrum coincides with the spectrum in the continuum and continuous
translation and rotation symmetries are restored in physical observables. This
is the first (analytic) construction of an exactly perfect lattice action at
finite correlation length.


title: P-wave meson properties with Wilson quarks

abstract:
  We describe two calculations involving P-wave mesons made of Wilson quarks:
the strong coupling constant $\alpha_s$ in the presence of two flavors of light
dynamical fermions and the mass and decay constant of the $a_1$ meson.


title: Rough Interfaces Beyond the Gaussian Approximation

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


title: Canonical Demon Monte Carlo Renormalization Group

abstract:
  We describe a method to compute renormalized coupling constants in a Monte
Carlo renormalization group calculation. It can be used, e.g., for lattice spin
or gauge models. The basic idea is to simulate a joint system of block spins
and canonical demons. Unlike the Microcanonical Renormalization Group of Creutz
et al. it avoids systematical errors in small volumes. We present numerical
results for the O(3) nonlinear sigma-model.


title:
Monopole condensation in the ground state of gauge theories: a disorder
  parameter

abstract:
  We construct a disorder parameter for dual superconductivity of the ground
state of $U(1)$ gauge theory.


title: Monopole condensation ans superconductivity: the $SU(2)$ case

abstract:
  We study the behaviour of a suitably defined disorder parameter, showing for
the first time monopole condenssation in the ground state of QCD.


title: Dynamics on the SU(2) fundamental domain

abstract:
  For SU(2) gauge theory on the three-sphere we focus on a subspace of modes of
the gauge field that contains the tunnelling paths and the sphalerons and on
which the energy functional is degenerate to second order in the fields. The
ultimate goal is to study the $\theta$-dependence of the low-lying states for
this model by imposing boundary conditions on the fundamental domain.


title: Some comments on Laplacian gauge fixing

abstract:
  Laplacian gauge fixing was introduced to find a unique representative of the
gauge orbit, which on the lattice could be implemented by a ``finite''
algorithm. What was still lacking was a perturbative formulation of this gauge,
which will be presented here. However, renormalizability is still to be
demonstrated. For torodial and spherical geometries a detailed comparison with
the Landau (or Coulomb) gauge will be made.


title:
London Penetration Length and String Tension in SU(2) Lattice Gauge
  Theory

abstract:
  We study the distribution of the color fields due to a static quark-antiquark
pair in SU(2) lattice gauge theory. We find evidence of dual Meissner effect.
We put out a simple relation between the penetration length and the string
tension.


title: Improving the Lattice QED Action

abstract:
  Strongly coupled QED is a model whose physics is dominated by short-ranged
effects. In order to assess which features of numerical simulations of the
chiral phase transition are universal and which are not, we have formulated a
quenched version of the model in which photon degrees of freedom are defined on
a lattice of spacing a, but fermions only on a lattice of spacing 2a. The
fermi-photon interaction is then obtained via a blocking procedure, whose
parameters allow a degree of control over the relative importance of short
wavelength modes. Results from a variety of models are presented; the critical
exponents delta and beta governing the transition appear to be independent of
the blocking, or even of whether a gauge-invariant action is used for the
photons.


title: The sphaleron energy for SU(2)-Higgs from cooling

abstract:
  The cooling algorithm for saddle points presented in ref. [1] is generalized
to obtain static classical solutions of the SU(2)-Higgs field theory in the
limit of infinite Higgs self-coupling. The sphaleron energy obtained via this
algorithm is ${\cal E}_{\rm sph}= 5.08(7)\,M_W/\alpha_W$ to be compared with
5.0707 obtained in the variational approach [2].


title: More on strongly coupled quenched QED

abstract:
  We study the critical region of lattice QED4 in the quenched approximation.
The issue of triviality is addressed by contrasting simulation results for
$<\bar\psi\psi>$ and for the susceptibilities with the predictions of two
critical scenarios -- powerlaw scaling, and triviality \`a la Nambu--Jona
Lasinio. We discriminate among the two possibilities with reasonable accuracy
and we confirm previous results for the critical point and exponents thanks to
new analysis strategies and good quality data. The interplay of chiral symmetry
breaking with the Goldstone mechanism is studied in detail, and some puzzling
features of past results are clarified. Chiral symmetry restoration is observed
in the spectrum: the candidate Goldstone boson decouples in the weak coupling
phase, while the propagators of the chiral doublets become degenerate. We also
present the first measurements of the full mesonic spectrum, relevant for the
study of flavour/ rotational symmetry restoration. The systematic effects
associated


title:
The electroweak phase transition: a non-perturbative lattice
  investigation

abstract:
  We present results obtained from a numerical investigation of the electroweak
phase transition in the SU(2)-Higgs model. The simulations are performed at two
values of the Higgs boson mass, $M_H\approx 20$ GeV and $M_H\approx 50$ GeV.
While the phase transition is of strongly first order at the smaller value of
the Higgs mass it weakens rapidly when the Higgs mass is increased. This is in
qualitative agreement with perturbation theory as the comparison of various
physical quantities shows.


title: The derivative expansion of the renormalization group

abstract:
  By writing the flow equations for the continuum Legendre effective action
(a.k.a. Helmholtz free energy) with respect to a particular form of smooth
cutoff, and performing a derivative expansion up to some maximum order, a set
of differential equations are obtained which at FPs (Fixed Points) reduce to
non-linear eigenvalue equations for the anomalous scaling dimension $\eta$.
Illustrating this by expanding (single component) scalar field theory, in two,
three and four dimensions, up to second order in derivatives, we show that the
method is a powerful and robust means of discovering and quantifying
non-perturbative continuum limits (continuous phase transitions).


title: ISU - Multigrid for computing propagators

abstract:
  The Iteratively Smoothing Unigrid algorithm (ISU), a new multigrid method for
computing propagators in Lattice Gauge Theory, is explained. The main idea is
to compute good (i.e.\ smooth) interpolation operators in an iterative way.
This method shows {\em no critical slowing down} for the 2-dimensional Laplace
equation in an SU(2) gauge field. First results for the Dirac-operator are also
shown.


title:
A new approach to instanton calculations in the O(3) nonlinear sigma
  model

abstract:
  We construct all instantons in the \nlsig\ on a cylindrical space-time, known
not to exist on a finite time interval. The scale parameter, $\rho$, is related
to the boundary condition in time. This may cure the $\rho\rightarrow0$
divergent instanton gas, through a proper inclusion of in and out states in the
path integral.


title: A proposal of a Renormalization Group transformation

abstract:
  We propose a family of renormalization group transformations characterized by
free parameters that may be tuned in order to reduce the truncation effects. As
a check we test them in the three dimensional XY model. The Schwinger--Dyson
equations are used to study the renormalization group flow.


title: Toward the QCD $\beta$ Function with Dynamical Wilson Fermions

abstract:
  We present data for the scaling behavior of lattice QCD with two flavors of
light Wilson fermions. This is done by matching $\pi$ n and $\rho$ masses at
the two lattice sizes of $16^3\times32 $ and $8^3\times16$. We find that at
$\beta=6/g^2\equiv5.3$ the matching does not occur over a range extending down
to $\beta=3.5$. For $\beta=5.5$ matching may be achieved at $\beta=4.8-4.9$,
leading to a $\Delta \beta =0.6-0.7$ which is higher than the perturbative
2-loop value of 0.45. In both cases we conclude that the simulations are very
far from the perturbative scaling region.


title: Charmonium spectroscopy with heavy Kogut-Susskind quarks

abstract:
  Charmonium spectroscopy with Kogut-Susskind valence quarks are carried out
for quenched QCD at $\beta=6.0$ and for two-flavor full QCD at $\beta=5.7$.
Results for 1P--1S mass splitting and estimates of
$\alpha^{(5)}_{\overline{MS}}(m_Z)$ are reported. Problems associated with
flavor breaking effects and finite size effects of $1P$ states are discussed.


title: Gauge theory of things alive and universal dynamics

abstract:
  Positing complex adaptive systems made of agents with relations between them
that can be composed, it follows that they can be described by gauge theories
similar to elementary particle theory and general relativity. By definition, a
universal dynamics is able to determine the time development of any such system
without need for further specification. The possibilities are limited, but one
of them - reproduction fork dynamics - describes DNA replication and is the
basis of biological life on earth. It is a universal copy machine and a
renormalization group fixed point. A universal equation of motion in continuous
time is also presented.

categories: hep-lat chao-dyn cond-mat gr-qc hep-ph hep-th nlin.CD q-bio


title: The Width of the Colour Flux Tube

abstract:
  We discuss and rederive in a general way the logarithmic growth of the mean
squared width of the colour flux tube as a function of the interquark
separation. Recent data on 3D $Z_2$ gauge theory, combined with high precision
data on the interface physics of the 3D Ising model fit nicely this behaviour
over a range of more than two orders of magnitude.


title: Roma versus Zaragoza

abstract:
  The Roma and Zaragoza actions for chiral fermions on the lattice are shown to
be essentially equivalent. The auxiliary fermion fields in the Roma model can
be integrated out, and the resulting action is a special case of the Zaragoza
approach. We use this result to perform a mean-field study of the phase diagram
of chiral Yukawa models in the Roma formulation.


title: New Method for the Extrapolation of Finite-Size Data to Infinite Volume

abstract:
  We present a simple and powerful method for extrapolating finite-volume Monte
Carlo data to infinite volume, based on finite-size-scaling theory. We discuss
carefully its systematic and statistical errors, and we illustrate it using
three examples: the two-dimensional three-state Potts antiferromagnet on the
square lattice, and the two-dimensional $O(3)$ and $O(\infty)$ $\sigma$-models.
In favorable cases it is possible to obtain reliable extrapolations (errors of
a few percent) even when the correlation length is 1000 times larger than the
lattice.


title: The Schr\"odinger functional in QCD

abstract:
  The Schr\"odinger functional in Wilson's lattice QCD leads to a sensible
classical continuum theory which can be taken as starting point for a
perturbative analysis. In dimensional regularization, the saddle point
expansion of the Schr\"odinger functional is performed to one-loop order of
perturbation theory. The divergences are partly cancelled by the usual coupling
constant and quark mass renormalization. An additional divergence can be
absorbed in a multiplicative renormalization of the quark boundary fields. The
corresponding boundary counterterm being a local polynomial in the fields we
confirm the general expectation expressed by Symanzik~\cite{Symanzik}.


title: Two-Dimensional $O(3)$ $\sigma$-Model up to Correlation Length $10^5$

abstract:
  We carry out a high-precision Monte Carlo simulation of the two-dimensional
$O(3)$-invariant $\sigma$-model at correlation lengths $\xi$ up to $\sim 10^5$.
Our work employs a new and powerful method for extrapolating finite-volume
Monte Carlo data to infinite volume, based on finite-size-scaling theory. We
compare the extrapolated data to the renormalization-group predictions. The
deviation from asymptotic scaling, which is $\approx 25\%$ at $\xi \sim 10^2$,
decreases to $\approx 4\%$ at $\xi \sim 10^5$.


title:
Study of a new simulation algorithm for dynamical quarks on the APE-100
  parallel computer

abstract:
  First results on the autocorrelation behaviour of a recently proposed fermion
algorithm by M. L\"uscher are presented and discussed. The occurence of
unexpected large autocorrelation times is explained. Possible improvements are
discussed.


title: B Physics From NRQCD With Dynamical Fermions

abstract:
  We present {\it preliminary} results for the spectrum and decay constants of
B mesons using NRQCD heavy and Wilson light quarks on configurations at
$\beta=5.6$ with two dynamical flavours of staggered fermions. All terms to
order $1/M_Q$ are included in the NRQCD action; matrix elements are corrected
to this order by calculating the small components of the heavy quark
propagator.


title: Quark Model from Lattice QCD

abstract:
  We study the valence approximation in lattice QCD of hadrons where the cloud
quarks and antiquarks are deleted by truncating the backward time propagation
(Z graphs) in the connected insertions. Whereas, the sea quarks are eliminated
via the quenched approximation and in the disconnected insertions. It is shown
that the ratios of isovector to isoscalar matrix elements in the nucleon
reproduce the SU(6) quark model predictions in a lattice QCD calculation. We
also discuss how the hadron masses are affected.


title: Perfect topological charge for asymptotically free theories

abstract:
  The classical equations of motion of the perfect lattice action in
asymptotically free $d=2$ spin and $d=4$ gauge models possess scale invariant
instanton solutions. This property allows the definition of a topological
charge on the lattice which is perfect in the sense that no topological defects
exist. The basic construction is illustrated in the $d=2$ O(3) non--linear
$\sigma$--model and the topological susceptibility is measured to high
precision in the range of correlation lengths $\xi \in (2 - 60)$. Our results
strongly suggest that the topological susceptibility is not a physical quantity
in this model.


title: Which Higgs-Yukawa systems can possess non-trivial fixed points

abstract:
  We argue that non-trivial fixed points bordering on the paramagnetic and
ferromagnetic phases are most likely to exist in the Higgs-Yukawa systems that
have a connected domain with the paramagnetic phase and no ferrimagnetic phase.
We find three examples of such systems; among them is the U(1) system with
naive fermions.


title: Absence of barriers in dynamical triangulation

abstract:
  Due to the unrecognizability of certain manifolds there must exist pairs of
triangulations of these manifolds that can only be reached from each other by
going through an intermediate state that is very large. This might reduce the
reliability of dynamical triangulation, because there will be states that will
not be reached in practice. We investigate this problem numerically for the
manifold $S^5$, which is known to be unrecognizable, but see no sign of these
unreachable states.


title: Spectrum and scaling in a strongly coupled fermion-gauge-scalar model

abstract:
  The strongly coupled lattice gauge models show an interesting mechanism of
dynamical mass generation. If a suitable continuum limit can be found, one may
think of it as an alternative to the Higgs mechanism. We present data on the
spectrum, obtained in the model with U(1) gauge symmetry with dynamical
fermions. They indicate that the fermion mass scales in the vicinity of the
whole chiral phase transition line. In contrast to this, the composite scalar
boson mass seems to get small only in the region near the endpoint E of the
Higgs phase transition. Thus this point is the most interesting candidate for
approaching the continuum limit. The masses of fermion--antifermion bound
states are also discussed.


title: Chiral transition in a strongly coupled fermion-gauge-scalar model

abstract:
  We report the recent results from the computer simulations of a
fermion-gauge-scalar model with dynamical chiral-symmetry breaking and chiral
transition induced by the scalar field. This model might be considered to be a
possible alternative to the Higgs mechanism of mass generation. A new scheme is
developed for detecting the chiral transition. Our results show with higher
precision than the earlier works that the chiral transition line joins the
Higgs phase transition line, separating the Higgs and Nambu (chiral-symmetry
breaking) phases. The end point of the Higgs transition with divergent
correlation lengths is therefore suitable for an investigation of the continuum
limit.


title:
The Microscopic Representation of Complex Macroscopic Phenomena
  (Critical Slowing Down - A Blessing in Disguise)

abstract:
  Many complex systems are representable as macroscopic set of elements which
interact by simple rules. The complex macroscopically relevant phenomena are
then the result of the generic emergence of a space-time multi-scale dynamics.
Critical Slowing Down labels the emerging global features and describes their
complex collective evolution. This paradigm is quite universal and extends to a
very wide range of systems and disciplines.


title: Dynamical Scaling from Multi-Scale Measurements

abstract:
  We present a new measure of the Dynamical Critical behavior: the "Multi-scale
Dynamical Exponent (MDE)"


title: New Results From UKQCD Using the Cray T3D: Measuring Gluonic Observables

abstract:
  We report on a set of simulations performed at several values of the lattice
spacing on the Cray T3D at Edinburgh. Different methods to extract the lattice
scale from the static quark potential are discussed.


title:
U(1) flux tube profiles from Hamiltonian lattice gauge theory using a
  random walk ground-state projector

abstract:
  We use a self-guided random walk to solve the ground-state problem of
Hamiltonian U(1) pure gauge theory in 2+1 dimensions in the string sector. By
making use of the electric-field representation, we argue that the spatial
distribution of the electric field can be more easily measured than in ordinary
Monte Carlo simulations.


title: Multibondic Cluster Algorithm

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


title: Ordered vs Disordered: Correlation Lengths of 2D Potts Models at \beta_t

abstract:
  We performed Monte Carlo simulations of two-dimensional $q$-state Potts
models with $q=10,15$, and $20$ and measured the spin-spin correlation function
at the first-order transition point $\beta_t$ in the disordered and ordered
phase. Our results for the correlation length $\xi_d(\beta_t)$ in the
disordered phase are compatible with an analytic formula. Estimates of the
correlation length $\xi_o(\beta_t)$ in the ordered phase yield strong numerical
evidence that $R \equiv \xi_o(\beta_t)/\xi_d(\beta_t) = 1$.


title: Regge's space-time skeletons and the quantization of 2d gravity

abstract:
  Regge's method for regularizing euclidean quantum gravity is applied to two
dimensional gravity. Using topologies with genus zero and two and a scale
invariant measure, we show that the Regge method fails to reproduce the values
of the string susceptibilities of the continuum model.