title: Hypercubic Smeared Links for Dynamical Fermions

abstract:
  We investigate a variant of hypercubic gauge link smearing where the SU(3)
projection is replaced with a normalization to the corresponding unitary group.
This smearing is differentiable and thus suitable for use in dynamical fermion
simulations using molecular dynamics type algorithms. We show that this
smearing is as efficient as projected hypercubic smearing in removing
ultraviolet noise from the gauge fields. We test the normalized hypercubic
smearing in dynamical improved (clover) Wilson and valence overlap simulations.


title: Can we study Quark Matter in the Quenched Approximation?

abstract:
  We study a quenched SU(2) lattice gauge theory in which, in an attempt to
distinguish between timelike and spacelike gauge fields, the gauge ensemble
{U_mu} is generated from a 3 dimensional gauge-Higgs model, the timelike link
variables being "reconstructed" from the Higgs fields. The resulting ensemble
is used to study quenched quark propagation with non-zero chemical potential
mu; in particular, the quark density, chiral and superfluid condensates, meson,
baryon and gauge-fixed quark propagators are all studied as functions of mu.
While it proves possible to alter the strength of the inter-quark interaction
by changing the parameters of the dimensionally reduced model, there is no
evidence for any region of parameter space where quarks exhibit deconfined
behaviour or thermodynamic observables scale as if there were a Fermi surface.


title:
Abelian dominance and the dual Meissner effect in local unitary gauges
  in SU(2) gluodynamics

abstract:
  Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we
observe for the first time Abelian dominance in the confining part of the
static potential in local unitary gauges such as the F12 gauge. We also study
the flux-tube profile between the quark and antiquark in these local unitary
gauges and find a clear signal of the dual Meissner effect. The Abelian
electric field is found to be squeezed into a flux tube by the monopole
supercurrent. This feature is the same as that observed in the non-local
maximally Abelian gauge. These results suggest that the Abelian confinement
scenario is gauge independent. Observing the important role of space-like
monopoles in the Polyakov gauge also indicates that the monopoles defined on
the lattice do not necessarily correspond to those proposed by 't Hooft in the
context of Abelian projection.


title:
Abelian dominance in local unitary gauges and without gauge-fixing in
  pure SU(2) QCD

abstract:
  We perform lattice Monte-Carlo simulations of pure SU(2) QCD using the
multi-level method. We find Abelian dominance in local unitary gauges such as
those diagonalizing a plaquette. A static potential described by Abelian link
fields alone gives us the same string tension as that of a non-Abelian
potential. Abelian dominance of the string tension and Abelian flux tube
profiles are observed also without gauge-fixing, i.e., without any Abelian
projection. On the basis of these results, we propose a simple
gauge-independent Abelian confinement scenario without any Abelian projection.
All color components of the non-Abelian field strength become Abelian dominant
in the infrared region. The Abelian dual Meissner effect works in any color
direction. Abelian neutral states in any color directions which are just
non-Abelian color-singlet can exist as a physical state. In this way, the
non-Abelian color confinement could be understood in the framework of the
Abelian dual Meissner effect.


title: The Sign Problem via Imaginary Chemical Potential

abstract:
  We calculate an analogue of the average phase factor of the staggered fermion
determinant at imaginary chemical potential. Our results from the lattice agree
well with the analytical predictions in the microscopic regime for both
quenched and phase-quenched QCD. We demonstrate that the average phase factor
in the microscopic domain is dominated by the lowest-lying Dirac eigenvalues.


title:
Hadronic form factors in Lattice QCD at small and vanishing momentum
  transfer

abstract:
  The introduction of partially twisted boundary conditions allows weak and
electromagnetic form factors to be evaluated at specified values of the
hadronic momenta (and hence momentum transfers) in lattice simulations. We
present and demonstrate this technique for the computation of the K->pi
semileptonic form factor at zero momentum transfer and for the electromagnetic
form factor of the pion at arbitrarily small momentum transfers. These
exploratory computations are carried out in full QCD with 3 flavours of sea
quarks, but with only two values of m_u=m_d which limits our ability to perform
the chiral extrapolations. The results should therefore be viewed primarily as
a demonstration of the feasibility of the method. For the K-> pi form factor we
compare the new technique to the conventional approach and for the pion form
factor we assess our results for very small momentum transfer with the help of
chiral perturbation theory.


title:
Non-perturbative improvement of the axial current with three dynamical
  flavors and the Iwasaki gauge action

abstract:
  We perform a non-perturbative determination of the improvement coefficient
c_A to remove O(a) discretization errors in the axial vector current in
three-flavor lattice QCD with the Iwasaki gauge action and the standard
O$(a)$-improved Wilson quark action. An improvement condition with a good
sensitivity to c_A is imposed at constant physics. Combining our results with
the perturbative expansion, c_A is now known rather precisely for 1/a \gtrsim
1.6 GeV.


title: Confining string and its widening in HP1 embedding approach

abstract:
  Structure of confining string in terms of the topological charge density and
the action density is studied in SU(2) Yang-Mills theory on the lattice using
HP1 sigma-model embedding approach. We find that the confining flux tube
noticeably suppresses both the topological charge and the action densities.
Beyond the string formation length the string cross section in terms of these
quantities is well described by a Gaussian profile. In both cases the squared
string width is found to be a logarithmic function of the string length
confirming the Luscher widening of the chromoelectric string. Characteristic
string scales in terms of the topological and action densities are estimated as
well.


title:
Spectral functions at small energies and the electrical conductivity in
  hot, quenched lattice QCD

abstract:
  In lattice QCD, the Maximum Entropy Method can be used to reconstruct
spectral functions from euclidean correlators obtained in numerical
simulations. We show that at finite temperature the most commonly used
algorithm, employing Bryan's method, is inherently unstable at small energies
and give a modification that avoids this. We demonstrate this approach using
the vector current-current correlator obtained in quenched QCD at finite
temperature. Our first results indicate a small electrical conductivity above
the deconfinement transition.

categories: hep-lat cond-mat.other hep-ph hep-th nucl-th


title: BB Potentials in Quenched Lattice QCD

abstract:
  The potentials between two B-mesons are computed in the heavy-quark limit
using quenched lattice QCD at $m_\pi\sim 400~{\rm MeV}$. Non-zero central
potentials are clearly evident in all four spin-isospin channels, (I,s_l) =
(0,0) , (0,1) , (1,0) , (1,1), where s_l is the total spin of the light degrees
of freedom. At short distance, we find repulsion in the $I\ne s_l$ channels and
attraction in the I=s_l channels. Linear combinations of these potentials that
have well-defined spin and isospin in the t-channel are found, in three of the
four cases, to have substantially smaller uncertainties than the potentials
defined with the s-channel (I,s_l), and allow quenching artifacts from single
hairpin exchange to be isolated. The BB*\pi coupling extracted from the
long-distance behavior of the finite-volume t-channel potential is found to be
consistent with quenched calculations of the matrix element of the isovector
axial-current. The tensor potentials in both of the s_l = 1 channels are found
to be consistent with zero within calculational uncertainties.


title: Gauge Field Strength Tensor from the Overlap Dirac Operator

abstract:
  We derive the classical continuum limit of the operator tr$_s \sigma_{\mu\nu}
D^{ov}(x,x)$ with $D^{ov}$ being the overlap Dirac operator and show that it
corresponds to the gauge field strength tensor $F_{\mu\nu}(x)$.


title:
Energies and radial distributions of B_s mesons - the effect of
  hypercubic blocking

abstract:
  This is a follow-up to our earlier work for the energies and the charge
(vector) and matter (scalar) distributions for S-wave states in a heavy-light
meson, where the heavy quark is static and the light quark has a mass about
that of the strange quark. We study the radial distributions of higher angular
momentum states, namely P- and D-wave states, using a "fuzzy" static quark. A
new improvement is the use of hypercubic blocking in the time direction, which
effectively constrains the heavy quark to move within a 2a hypercube (a is the
lattice spacing).
  The calculation is carried out with dynamical fermions on a 16^3 times 32
lattice with a lattice spacing approximately 0.10 fm generated using the
non-perturbatively improved clover action. The configurations were generated by
the UKQCD Collaboration using lattice action parameters beta = 5.2, c_SW =
2.0171 and kappa = 0.1350.
  In nature the closest equivalent of this heavy-light system is the B_s meson.
Attempts are now being made to understand these results in terms of the Dirac
equation.


title: Mixed Action Lattice Spacing Effects on the Nucleon Axial Charge

abstract:
  We study the nucleon axial charge in the chiral perturbation theory for a
mixed lattice action of Ginsparg-Wilson valence quarks and staggered sea
quarks. In particular, we investigate the lattice spacing $a^2$-dependence of
the neutron to proton axial transition matrix element. By using the known
low-energy constants (LEC's) and an estimated value of a new LEC which appears
in the calculation, we see a large lattice spacing effect on $g_A$.


title: Domain wall filters

abstract:
  We propose using the extra dimension separating the domain walls carrying
lattice quarks of opposite handedness to gradually filter out the ultraviolet
fluctuations of the gauge fields that are felt by the fermionic excitations
living in the bulk. This generalization of the homogeneous domain wall
construction has some theoretical features that seem nontrivial.


title: Pseudoscalar and vector meson form factors from lattice QCD

abstract:
  We present a study of the pseudoscalar and vector meson form factors,
calculated using the Fat-Link Irrelevant Clover (FLIC) action in the framework
of Quenched Lattice QCD. Of particular interest is the determination of a
negative quadrupole moment, indicating that the $\rho$ meson is not spherically
symmetric.


title: Hadron Scattering in an Asymmetric Box

abstract:
  We propose to study hadron-hadron scattering using lattice QCD in an
asymmetric box which allows one to access more non-degenerate low-momentum
modes for a given volume. The conventional L\"{u}scher's formula applicable in
a symmetric box is modified accordingly. To illustrate the feasibility of this
approach, pion-pion elastic scattering phase shifts in the I=2, J=0 channel are
calculated within quenched approximation using improved gauge and Wilson
fermion actions on anisotropic lattices in an asymmetric box. After the chiral
and continuum extrapolation, we find that our quenched results for the
scattering phase shifts in this channel are consistent with the experimental
data when the three-momentum of the pion is below 300MeV. Agreement is also
found when compared with previous theoretical results from lattice and other
means. Moreover, with the usage of asymmetric volume, we are able to compute
the scattering phases in the low-momentum range (pion three momentum less than
about 350MeV in the center of mass frame) for over a dozen values of the pion
three-momenta, much more than using the conventional symmetric box with
comparable volume.


title:
Phase diagram of the three dimensional Thirring model - A Monte Carlo
  study

abstract:
  Certain approximate solutions of the continuum Schwinger-Dyson Equations
(SDEs) predict chiral symmetry breaking in the 3d Thirring model when the
number of fermion flavors N_f<4.32 whereas others predict symmetry breaking for
all N_f. Our results from Monte Carlo simulations with N_f=6, predict a second
order chiral phase transition. The critical coupling in this case corresponds
to an ultra-violet fixed point of the renormalization group defining a
non-trivial continuum limit. Further, our numerical simulations provide an
estimate for the critical number of fermion flavors, N_fc \approx 6.5.


title: Simulating Dense Matter

abstract:
  I review the Sign Problem hindering lattice QCD simulations of dense baryonic
matter, focussing where possible on its physical relevance. The possibility of
avoiding the Sign Problem via a duality transformation is also briefly
considered. Finally, I review evidence for deconfinement at non-zero quark
density in recent simulations of Two Color QCD.


title:
Spectral sums of the Dirac-Wilson Operator and their relation to the
  Polyakov loop

abstract:
  We investigate and compute spectral sums of the Wilson lattice Dirac operator
for quenched SU(3) gauge theory. It is demonstrated that there exist sums which
serve as order parameters for the confinement-deconfinement phase transition
and get their main contribution from the IR end of the spectrum. They are
approximately proportional to the Polyakov loop. In contrast to earlier studied
spectral sums some of them are expected to have a well-defined continuum limit.


title: Scalar-Quark Systems and Chimera Hadrons in SU(3)_c Lattice QCD

abstract:
  Light scalar-quarks \phi (colored scalar particles or idealized diquarks) and
their color-singlet hadronic states are studied with quenched SU(3)_c lattice
QCD in terms of mass generation in strong interaction without chiral symmetry
breaking. We investigate ``scalar-quark mesons'' \phi^\dagger \phi and
``scalar-quark baryons'' \phi\phi\phi which are the bound states of
scalar-quarks \phi. We also investigate the bound states of scalar-quarks \phi
and quarks \psi, i.e., \phi^\dagger \psi, \psi\psi\phi and \phi\phi\psi, which
we name ``chimera hadrons''. All the new-type hadrons including \phi are found
to have a large mass even for zero bare scalar-quark mass m_\phi=0 at
a^{-1}\simeq 1GeV. We find that the constituent scalar-quark and quark picture
is satisfied for all the new-type hadrons. Namely, the mass of the new-type
hadron composed of m \phi's and n \psi's, M_{{m}\phi+{n}\psi}, satisfies
M_{{m}\phi+{n}\psi}\simeq {m} M_\phi +{n} M_\psi, where M_\phi and M_\psi are
the constituent scalar-quark and quark mass, respectively. M_\phi at m_\phi=0
estimated from these new-type hadrons is 1.5-1.6GeV, which is larger than that
of light quarks, M_\psi\simeq 400{\rm MeV}. Therefore, in the systems of
scalar-quark hadrons and chimera hadrons, scalar-quarks acquire large mass due
to large quantum corrections by gluons. Together with other evidences of mass
generations of glueballs and charmonia, we conjecture that all colored
particles generally acquire a large effective mass due to dressed gluon
effects.


title: Infra-red divergences in the large-N expansion

abstract:
  We investigate a vectorial O(N) model with a generic nearest-neighbor
interaction W(\bsigma_i\cdot \bsigma_j) (depending on {\cal N} tunable
parameters), a Yukawa (and Gross Neveu) model with N_f fermions at finite
temperature and the vectorial \phi^6 model, in the large N (N_f) limit. All
this models exhibit a Mean Field critical point for N=\infinity. When 1/N
fluctuations are included, infra red divergences appear near the critical
point. In the framework of a generalized 1/N expansion we show that these
divergences are related to a universal crossover mechanism between the Mean
Field universality class (N=\infinity) and the nonclassical one for
N<\infinity. For the generic nearest-neighbor interaction multicritical points
are also investigated.


title: Speeding up Domain Wall Fermion Algorithms using QCDLAB

abstract:
  Simulating lattice QCD with chiral fermions and indeed using Domain Wall
Fermions continues to be challenging project however large are concurrent
computers. One obvious bottleneck is the slow pace of prototyping using the low
level coding which prevails in most, if not all, lattice projects. Recently, we
came up with a new proposal, namely QCDLAB, a high level language interface,
which we believe will boost our endeavours to rapidly code lattice prototype
applications in lattice QCD using MATLAB/OCTAVE language and environment. The
first version of the software, QCDLAB 1.0 offers the general framework on how
to achieve this goal by simulating set of the lattice Schwinger model {\tt
http://phys.fshn.edu.al/qcdlab.html}. In this talk we introduce QCDLAB 1.1,
which extends QCDLAB 1.0 capabilities for real world lattice computations with
Wilson and Domain Wall fermions.


title:
Scaling behavior and positivity violation of the gluon propagator in
  full QCD

abstract:
  The Landau-gauge gluon propagator is studied using the coarse and fine
dynamical MILC configurations. The effects of dynamical quarks are clearly
visible and lead to a reduction of the nonperturbative infrared enhancement
relative to the quenched case. Lattice spacing effects are studied and found to
be small. The gluon spectral function is shown to clearly violate positivity in
both quenched and full QCD.


title: Low-lying Dirac eigenmodes and monopoles in 4D compact QED

abstract:
  We study the properties of low-lying Dirac modes in quenched compact QED at
$\beta$=0.99, 1.01 and 1.03, employing $12^3\times 12$ lattices and the overlap
formalism for the fermion action. We pay special attention to the spatial
distributions of the low-lying Dirac modes. Near-zero modes are found to have
universal anti-correlations with monopole currents below/above the critical
$\beta$. We also study the nearest-neighbor level spacing distribution of Dirac
eigenvalues and find a signal of a Wigner-Poisson transition. We make a
possible speculation on the chiral phase transition in 4D compact QED.


title: How to Put a Heavier Higgs on the Lattice

abstract:
  Lattice work, exploring the Higgs mass triviality bound, seems to indicate
that a strongly interacting scalar sector in the minimal standard model cannot
exist while low energy QCD phenomenology seems to indicate that it could. We
attack this puzzle using the 1/N expansion and discover a simple criterion for
selecting a lattice action that is more likely to produce a heavy Higgs
particle. Our large $N$ calculation suggests that the Higgs mass bound might be
around $850 GeV$, which is about 30% higher than previously obtained.


title: Spectral Density Study of the SU(3) Deconfining Phase Transition

abstract:
  We present spectral density reweighting techniques adapted to the analysis of
a time series of data with a continuous range of allowed values. In a first
application we analyze action and Polyakov line data from a Monte Carlo
simulation on $L_t L^3 (L_t=2,4)$ lattices for the SU(3) deconfining phase
transition. We calculate partition function zeros, as well as maxima of the
specific heat and of the order parameter susceptibility. Details and warnings
are given concerning i) autocorrelations in computer time and ii) a reliable
extraction of partition function zeros. The finite size scaling analysis of
these data leads to precise results for the critical couplings $\beta_c$, for
the critical exponent $\nu$ and for the latent heat $\triangle s$. In both
cases ($L_t=2$ and 4), the first order nature of the transition is
substantiated.


title: Vectorized Cluster Search

abstract:
  Contrary to conventional wisdom, the construction of clusters on a lattice
can easily be vectorized, namely over each ``generation'' in a breadth first
search. This applies directly to, e.g., the {\it single cluster} variant of the
Swendsen-Wang algorithm. On a Cray Y-MP, total CPU time was reduced by a factor
3.5 -- 7 in actual applications.


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

abstract:
  We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC)
algorithm with piecewise-constant interpolation applied to the two-dimensional
O(4)-symmetric nonlinear $\sigma$-model [= SU(2) principal chiral model], on
lattices up to $256 \times 256$. We find a dynamic critical exponent
$z_{int,{\cal M}^2} = 0.60 \pm 0.07$ for the W-cycle and $z_{int,{\cal M}^2} =
1.13 \pm 0.11$ for the V-cycle, compared to $z_{int,{\cal M}^2} = 2.0 \pm 0.15$
for the single-site heat-bath algorithm (subjective 68% confidence intervals).
Thus, for this asymptotically free model, critical slowing-down is greatly
reduced compared to local algorithms, but not completely eliminated. For a $256
\times 256$ lattice, W-cycle MGMC is about 35 times as efficient as a
single-site heat-bath algorithm.


title: Monte Carlo Simulations of Higgs-Fermion Systems

abstract:
  To gain understanding of the Higgs-fermion sector of the standard model, we
study the one-component $Z_2$ symmetric and the four-component O(4) symmetric
scalar models coupled to staggered fermions using the hybrid Monte Carlo
algorithm. We map out the phase diagrams, and show that the $Z_2$ model has a
tree level perturbative behaviour at all points in the broken phase. The O(4)
model on the other hand is shown to have two characteristically different
behaviours; one for large Yukawa couplings where the fermions get infinitely
heavy and decouple in the continuum limit, and one for small Yukawa couplings
where the fermions remain light. For very small Yukawa couplings the fermions
show the expected tree level perturbative behaviour and for larger values the
influence of the fermions becomes substantial. After estimating the finite size
effects at small Yukawa couplings we make relatively accurate measurements of
the scalar mass and wave function renormalization constants at the point
$\kappa=0.0$ and $y=0.85-0.95$. Even though this is not the largest value
possible for the Yukawa coupling we are able to show that the bound of the
Higgs mass will move up significantly, from around $600 GeV$ to around $900
GeV$, by including fermions in the model. Likewise we show that a bound can be
put on the fermion mass, around $200 GeV$. The largest value of the bare Yukawa
coupling is obtained at rather large negative $\kappa$. Due to bad convergence
rates in the inversion of the fermion matrix, which is needed in the updating
procedure, this region has not been possible to investigate.


title:
A Study of Symmetry Restoration at Finite Temperature in the O(4) Model
  Using Anisotropic Lattices

abstract:
  Results of investigations of the O(4) spin model at finite temperature using
anisotropic lattices are presented. In both the large $N$ approximation and the
numerical simulations using the Wolff cluster algorithm we find that the ratio
of the symmetry restoration temperature $T_{\rm SR}$ to the Higgs mass $m_{\rm
H}$ is independent of the anisotropy. We obtain a lower bound of $0.59 \pm
0.04$ for the ratio, $T_{\rm SR}/m_{\rm H}$, at $m_{\rm H}a \simeq 0.5$, which
is lowered further by about 10% at $m_{\rm H}a \simeq 1.$


title:
Dynamic Critical Behaviour of Wolff's Algorithm for $RP^N$
  $\sigma$-Models

abstract:
  We study the performance of a Wolff-type embedding algorithm for $RP^N$
$\sigma$-models. We find that the algorithm in which we update the embedded
Ising model \`a la Swendsen-Wang has critical slowing-down as $z_\chi \approx
1$. If instead we update the Ising spins with a perfect algorithm which at
every iteration produces a new independent configuration, we obtain $z_\chi
\approx 0$. This shows that the Ising embedding encodes well the collective
modes of the system, and that the behaviour of the first algorithm is connected
to the poor performance of the Swendsen-Wang algorithm in dealing with a
frustrated Ising model.


abstract:
  The cutoff dependence of the Scalar Sector of the Minimal Standard Model can
result in an increase of the existing triviality bound estimates of the Higgs
mass. We present a large $N$ calculation and some preliminary N=4 results that
suggest that the increase can be as large as 30%, resulting to a bound of about
850 G eV.


title: QCD Hadron Spectroscopy with Staggered Dynamical Quarks at $\beta = 5.6$

abstract:
  We present preliminary results from the 1991 HEMCGC simulations with
staggered dynamical fermions on a $16^3 \times 32$ lattice at $\beta = 5.6$
with sea quark masses $am_q = 0.025$ and 0.01. The spectroscopy was done both
for staggered valence quarks with mass equal to the sea quark masses and for
Wilson valence quarks at six different values for $\kappa$, 0.1320, 0.1410,
0.1525, 0.1565, 0.1585, and 0.1600. In addition to the measurements performed
in our earlier work, we also measured the $\Delta$ and other `extended' hadrons
for staggered valence quarks and pseudo-scalar decay constants and vector meson
matrix elements, the wave function at the origin, for Wilson valence quarks.


title:
Path Integrals and Voronin's Theorem on the Universality of the Riemann
  Zeta Function

abstract:
  We explore a new approach to the path integral for a latticized quantum
theory. This talk is based on work with N. Khuri and H. Ren.


title: On the Dynamics of Light Wilson Quarks

abstract:
  We describe recent results obtained as part of the High Energy Monte Carlo
Grand Challenge (HEMCGC) project concerning the behaviour of lattice QCD with
light dynamical Wilson quarks. We show that it is possible to reach regions of
parameter space with light pions $m_\pi\ll0.2/a$, but that the equilibration
time for such a system is at least of the order of 1,000 unit-length Hybrid
Monte Carlo (HMC) trajectories (about a Gigaflop/sec-year). If the Hybrid
Molecular Dynamics (HMD) algorithm is used with the same parameters it gives
incorrect results.


title:
Monte Carlo Calculation of the Surface Free Energy for the 2d 7-state
  Potts Model, and an Estimate for 4d SU(3) Gauge Theory

abstract:
  Using the recently proposed multicanonical ensemble, we perform Monte Carlo
simulation for the 2d 7-state Potts model and calculate its surface free energy
density (surface tension) to be $2 f^s = 0.0241 \pm 0.0010$. This is an order
of magnitude smaller than other estimates in the recent literature. Relying on
existing Monte Carlo data, we also give a preliminary estimate for the surface
tension of 4d SU(3) lattice gauge theory with $L_t=2$.


title:
Random Walks and the Correlation Length Critical Exponent in Scalar
  Quantum Field Theory

abstract:
  The distance scale for a quantum field theory is the correlation length
$\xi$, which diverges with exponent $\nu$ as the bare mass approaches a
critical value. If $t=m^{2}-m_{c}^{2}$, then $\xi=m_{P}^{-1} \sim t^{-\nu}$ as
$t \to 0$. The two-point function of a scalar field has a random walk
representation. The walk takes place in a background of fluctuations (closed
walks) of the field itself. We describe the connection between properties of
the walk and of the two-point function. Using the known behavior of the two
point function, we deduce that the dimension of the walk is $d_{w}=\phi / \nu$
and that there is a singular relation between $t$ and the energy per unit
length of the walk $\theta \sim t^{\phi}$ that is due to the singular behavior
of the background at $t=0$. ($\phi$ is a computable crossover exponent.)


title:
Thermodynamics of Lattice QCD with 2 Light Dynamical (Staggered) Quark
  Flavours on a $16^3\times 8$ Lattice

abstract:
  Lattice QCD with 2 light staggered quark flavours is being simulated on a
$16^3\times8$ lattice to study the transition from hadronic matter to a quark
gluon plasma. We have completed runs at $m_q=0.0125$ and are extending this to
$m_q=0.00625$. We also examine the addition of a non-dynamical "strange" quark.
Thermodynamic order parameters are being measured across the transition and
further into the plasma phase, as are various screening lengths. No evidence
for a first order transition is seen, and we estimate the transition
temperature to be $TY_c=143(7) MeV$.


title:
Multicanonical Ensemble: A New Approach to Simulate First-order Phase
  Transitions

abstract:
  Relying on the recently proposed multicanonical algorithm, we present a
numerical simulation of the first order phase transition in the 2d 10-state
Potts model on lattices up to sizes $100\times100$. It is demonstrated that the
new algorithm $lacks$ an exponentially fast increase of the tunneling time
between metastable states as a function of the linear size $L$ of the system.
Instead, the tunneling time diverges approximately proportional to $L^{2.65}$.
Thus the computational effort as counted per degree of freedom for generating
an independent configuration in the unstable region of the model rises
proportional to $V^{2.3}$, where $V$ is the volume of the system. On our
largest lattice we gain more than two orders of magnitude as compared to a
standard heat bath algorithm. As a first physical application we report a high
precision computation of the interfacial tension.


title: Is there a $\rho$ in the O(4) $\lambda \phi^4_4$ theory?

abstract:
  A Monte Carlo simulation of the O(4) $\lambda \phi^4$ theory in the broken
phase is performed on a hypercubic lattice in search of an I=1, J=1 resonance.
The region of the cutoff theory where the interaction is strong is investigated
since it is there that a resonance would be expected to have a better chance to
form. In that region the presence of an I=1, J=1 resonance with mass below the
cutoff is excluded.


title: Multimagnetical Simulations

abstract:
  We modified the recently proposed multicanonical MC algorithm for the case of
a magnetic field driven order--order phase transition. We test this {\it
multimagnetic} Monte Carlo algorithm for the D=2 Ising model at $\beta=0.5$ and
simulate square lattices up to size $100 \times 100$. On these lattices with
periodic boundary conditions it is possible to enhance the appearance of
order-order interfaces during the simulation by many orders of magnitude as
compared to the standard Monte Carlo simulation.


title: A New Approach to Spin Glass Simulations

abstract:
  We present a recursive procedure to calculate the parameters of the recently
introduced multicanonical ensemble and explore the approach for spin glasses.
Temperature dependence of the energy, the entropy and other physical quantities
are easily calculable and we report results for the zero temperature limit. Our
data provide evidence that the large $L$ increase of the ergodicity time is
greatly improved. The multicanonical ensemble seems to open new horizons for
simulations of spin glasses and other systems which have to cope with
conflicting constraints.


title:
A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional
  Quantum Gravity

abstract:
  We perform Monte Carlo simulations using the Wolff cluster algorithm of the
q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of
spherical topology with up to 5000 nodes. We find that the measured critical
exponents are in reasonable agreement with those from the exact solution of the
Ising model and with those calculated from KPZ scaling for q=3,4 where no exact
solution is available. Using Binder's cumulant we find that the q=10 Potts
model displays a first order phase transition on a dynamical graph, as it does
on a fixed lattice. We also examine the internal geometry of the graphs
generated in the simulation, finding a linear relationship between ring length
probabilities and the central charge of the Potts model


title: Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity

abstract:
  We perform Monte Carlo simulations using the Wolff cluster algorithm of {\it
multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of
spherical topology in order to investigate the $c>1$ region of two-dimensional
quantum gravity. Contrary to naive expectation we find no obvious signs of
pathological behaviour for $c>1$. We discuss the results in the light of
suggestions that have been made for a modified DDK ansatz for $c>1$.


title:
Critical Behavior of Dynamically Triangulated Quantum Gravity in Four
  Dimensions

abstract:
  We performed detailed study of the phase transition region in Four
  Dimensional Simplicial Quantum Gravity, using the dynamical triangulation
approach. The phase transition between the Gravity and
  Antigravity phases turned out to be asymmetrical, so that we observed the
scaling laws only when the Newton constant approached the critical value from
perturbative side. The curvature susceptibility diverges with the scaling index
$-.6$. The physical (i.e. measured with heavy particle propagation) Hausdorff
dimension of the manifolds, which is
  2.3 in the Gravity phase and 4.6 in the Antigravity phase, turned out to be 4
at the critical point, within the measurement accuracy. These facts indicate
the existence of the continuum limit in Four
  Dimensional Euclidean Quantum Gravity.


title: Microcanonical cluster algorithms

abstract:
  I propose a numerical simulation algorithm for statistical systems which
combines a microcanonical transfer of energy with global changes in clusters of
spins. The advantages of the cluster approach near a critical point augment the
speed increases associated with multi-spin coding in the microcanonical
approach. The method also provides a limited ability to tune the average
cluster size.


title: Point-Split Lattice Operators for B Decays

abstract:
  The matrix element which determines the B meson decay constant can be
measured on the lattice using an effective field theory for heavy quarks.
Various discretizations of the heavy-light bilinears which appear in this and
other B decay matrix elements are possible. The heavy-light bilinear currently
used for the determination of the B meson decay constant on the lattice suffers
a substantial one-loop renormalization. In this paper, we compute the one-loop
renormalizations of the discretizations in which the heavy and light fields in
the bilinear are separated by one lattice spacing, and discuss their
application. Readers of this paper may also be interested in our paper on the
application of Symanzik's improvement program to heavy-light currents (paper
number 9203221 on hep-ph).


title: Chiral Perturbation Theory for the Quenched Approximation of QCD

abstract:
  [This version is a minor revision of a previously submitted preprint. Only
references have been changed.] We describe a technique for constructing the
effective chiral theory for quenched QCD. The effective theory which results is
a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and
fermions, and with a definite (though slightly peculiar) set of Feynman rules.
The straightforward application of these rules gives automatic cancellation of
diagrams which would arise from virtual quark loops. The techniques are used to
calculate chiral logarithms in $f_K/f_\pi$, $m_\pi$, $m_K$, and the ratio of
$\langle{\bar s}s\rangle$ to $\langle{\bar u}u\rangle$. The leading
finite-volume corrections to these quantities are also computed. Problems for
future study are described.


title:
Hadron Spectrum in QCD with Valence Wilson Fermions and Dynamical
  Staggered Fermions at $6/g^2=5.6

abstract:
  We present an analysis of hadronic spectroscopy for Wilson valence quarks
with dynamical staggered fermions at lattice coupling $6/g^2 = \beta=5.6$ at
sea quark mass $am_q=0.01$ and 0.025, and of Wilson valence quarks in quenched
approximation at $\beta=5.85$ and 5.95, both on $16^3 \times 32$ lattices. We
make comparisons with our previous results with dynamical staggered fermions at
the same parameter values but on $16^4$ lattices doubled in the temporal
direction.


title: Spectrum of Relativistic Fermions in a 2d Doped Lattice

abstract:
  Motivated by some previous work on fermions on random lattices and by
suggestions that impurities could trigger parity breaking in 2d crystals, we
have analyzed the spectrum of the Dirac equation on a two dimensional square
lattice where sites have been removed randomly --- a doped lattice. We have
found that the system is well described by a sine-Gordon action. The solitons
of this model are the lattice fermions, which pick a quartic interaction due to
the doping and become Thirring fermions. They also get an effective mass
different from the lagrangian mass. The system seems to exhibit spontaneous
symmetry breaking, exactly as it happens for a randomly triangulated lattice.
The associated ``Goldstone boson" is the sine-Gordon scalar. We argue, however,
that the peculiar behaviour of the chiral condensate is due to finite size
effects.


title:
Influence of the Measure on Simplicial Quantum Gravity in Four
  Dimensions

abstract:
  We investigate the influence of the measure in the path integral for
Euclidean quantum gravity in four dimensions within the Regge calculus. The
action is bounded without additional terms by fixing the average lattice
spacing. We set the length scale by a parameter $\beta$ and consider a scale
invariant and a uniform measure. In the low $\beta$ region we observe a phase
with negative curvature and a homogeneous distribution of the link lengths
independent of the measure. The large $\beta$ region is characterized by
inhomogeneous link lengths distributions with spikes and positive curvature
depending on the measure.


title: Phenomenology with Wilson fermions using smeared sources

abstract:
  We investigate the use of two types of non-local (``smeared'') sources for
quark propagators in quenched lattice QCD at $\beta=6.0$ using Wilson fermions
at $\kappa=0.154$ and $0.155$. We present results for the hadron mass spectrum,
meson decay constants, quark masses, the chiral condensate and the quark
distribution amplitude of the pion. The use of smeared sources leads to a
considerable improvement over previous results. We find a disturbing
discrepancy between the baryon spectra obtained using Wuppertal and wall
sources. We find good signals in the ratio of correlators used to calculate the
quark mass and the chiral condensate and show that the extrapolation to the
chiral limit is smooth.


title: Scalar and axial matrix elements of the nucleon: sea quark content

abstract:
  Sea quark contributions to the scalar density and the axial current matrix
elements of the nucleon are studied in lattice qcd with two flavours of
dynamical wilson fermions. the results are compared to trends in heavy quark
mass expansions, and contrasted with the numbers obtained using dynamical
staggered fermions.


title: The Free Energy of Spherical Bubbles in Lattice SU(3) Gauge Theory

abstract:
  We study the coefficients of the expansion $F(R) = 1/3 c_3 R^3 + 1/2 c_2 R^2
+ c_1 R$ of the free energy of spherical bubbles at $T=T_c$ in pure glue QCD
using lattice Monte Carlo techniques. The coefficient $c_3$ vanishes at $T=T_c$
and our results suggest that the sign and the order of magnitude of $c_1$ is in
agreement with the value $c_1=\pm 32\pi T_c^2/9$ (- for hadronic bubbles in
quark phase, + for quark bubbles in hadronic phase) computed by Mardor and
Svetitsky from the MIT bag model. The parameter $c_2$ is small in agreement
with earlier determinations.


title: Multigrid Methods in Lattice Field Computations

abstract:
  The multigrid methodology is reviewed. By integrating numerical processes at
all scales of a problem, it seeks to perform various computational tasks at a
cost that rises as slowly as possible as a function of $n$, the number of
degrees of freedom in the problem. Current and potential benefits for lattice
field computations are outlined. They include: $O(n)$ solution of Dirac
equations; just $O(1)$ operations in updating the solution (upon any local
change of data, including the gauge field); similar efficiency in gauge fixing
and updating; $O(1)$ operations in updating the inverse matrix and in
calculating the change in the logarithm of its determinant; $O(n)$ operations
per producing each independent configuration in statistical simulations
(eliminating CSD), and, more important, effectively just $O(1)$ operations per
each independent measurement (eliminating the volume factor as well). These
potential capabilities have been demonstrated on simple model problems.
Extensions to real life are explored.


title: Blockspin Cluster Algorithms for Quantum Spin Systems

abstract:
  Cluster algorithms are developed for simulating quantum spin systems like the
one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The
corresponding two- and three-dimensional classical spin models with four-spin
couplings are maped to blockspin models with two-blockspin interactions.
Clusters of blockspins are updated collectively. The efficiency of the method
is investigated in detail for one-dimensional spin chains. Then in most cases
the new algorithms solve the problems of slowing down from which standard
algorithms are suffering.


title: Acceptance Rates in Multigrid Monte Carlo

abstract:
  An approximation formula is derived for acceptance rates of nonlocal
Metropolis updates in simulations of lattice field theories. The predictions of
the formula agree quite well with Monte Carlo simulations of 2-dimensional Sine
Gordon, XY and phi**4 models. The results are consistent with the following
rule: For a critical model with a fundamental Hamiltonian H(phi) sufficiently
high acceptance rates for a complete elimination of critical slowing down can
only be expected if the expansion of < H(phi+psi) > in terms of the shift psi
contains no relevant term (mass term).


title:
Decoupling a Fermion Whose Mass Comes from a Yukawa Coupling:
  Nonperturbative Considerations

abstract:
  Perturbative analyses seem to suggest that fermions whose mass comes solely
from a Yukawa coupling to a scalar field can be made arbitrarily heavy, while
the scalar remains light. The effects of the fermion can be summarized by a
local effective Lagrangian for the light degrees of freedom. Using weak
coupling and large N techniques, we present a variety of models in which this
conclusion is shown to be false when nonperturbative variations of the scalar
field are considered. The heavy fermions contribute nonlocal terms to the
effective action for light degrees of freedom. This resolves paradoxes about
anomalous and nonanomalous symmetry violation in these models. Application of
these results to lattice gauge theory imply that attempts to decouple lattice
fermion doubles by the method of Swift and Smit cannot succeed, a result
already suggested by lattice calculations.


title: Scaling topological charge in the CP^3 spin model

abstract:
  The CP^3 spin model is simulated at large correlation lengths in two
dimensions. An overrelaxation algorithm is employed which yields reduced
critical slowing down with dynamical exponents z around unity. We compare our
results with recent multigrid data on the massgap m and the spin susceptibility
and confirm the absence of asymptotic scaling. As a new result we find scaling
for the universal topological susceptibility with values extrapolating to chi_t
/ m^2 = 0.156(2) in the continuum limit.


title:
Chiral Invariance and Species Doublers in Generic Fermion Models on the
  Lattice

abstract:
  Discussions are made on the structures of chirally invariant lattice actions
without any restriction of hermiticity. With the help of the Ward-Takahashi
identity a general conclusion can be derived that there must be species
doublers in any chirally invariant model provided that the model is chosen as
well-regularized, that is, there is no singularity in the propagator after
introducing fermion mass on the lattice. Various examples are discussed to pick
up better models defined in the sense that the number of species doubler is
smaller than that of the naive Dirac action.


title: Non--perturbative bounds on the Higgs mass in the minimal standard model

abstract:
  This is a slightly extended version of the talk delivered at the Topical
Workshop ``Non perturbative aspects of chiral gauge theories'', Accademia
Nazionale dei Lincei, Roma, 9-11 March, 1992. Abstract: The Higgs mass in the
minimal standard model is bounded by triviality and vacuum stability in the
range 50--100 $GeV$ to 700--900 $GeV$. Recent results will be presented in
brief and directions for future work will be proposed.


title:
Spontaneous symmetry breaking on the lattice generated by Yukawa
  interaction

abstract:
  We study by numerical simulation a lattice Yukawa model with naive fermions
at intermediate values of the Yukawa coupling $y$ when the nearest neighbour
coupling $\kp$ of the scalar field $\Phi$ is very weakly ferromagnetic ($\kp
\approx 0$) or even antiferromagnetic ($\kappa < 0$) and the nonvanishing value
of $\vev$ is generated by the Yukawa interaction. The renormalized Yukawa
coupling $y_R$ achieves here its maximal value and this $y$-region is thus of
particular importance for lattice investigations of strong Yukawa interaction.
However, here the scalar field propagators have a very complex structure caused
by fermion loop corrections and by the proximity of phases with
antiferromagnetic properties. We develop methods for analyzing these
propagators and for extracting the physical observables. We find that going
into the negative $\kp$ region, the scalar field renormalization constant
becomes small and $y_R$ does not seem to exceed the unitarity bound, making the
existence of a nontrivial fixed point in the investigated Yukawa model quite
unlikely.


title: Wolff-Type Embedding Algorithms for General Nonlinear $\sigma$-Models

abstract:
  We study a class of Monte Carlo algorithms for the nonlinear $\sigma$-model,
based on a Wolff-type embedding of Ising spins into the target manifold $M$. We
argue heuristically that, at least for an asymptotically free model, such an
algorithm can have dynamic critical exponent $z \ll 2$ only if the embedding is
based on an (involutive) isometry of $M$ whose fixed-point manifold has
codimension 1. Such an isometry exists only if the manifold is a discrete
quotient of a product of spheres. Numerical simulations of the idealized
codimension-2 algorithm for the two-dimensional $O(4)$-symmetric $\sigma$-model
yield $z_{int,{\cal M}^2} = 1.5 \pm 0.5$ (subjective 68\% confidence interval),
in agreement with our heuristic argument.


title: Rigorous QCD Predictions for Decays of P-Wave Quarkonia

abstract:
  Rigorous QCD predictions for decay rates of the P-wave states of heavy
quarkonia are presented. They are based on a new factorization theorem which is
valid to leading order in the heavy quark velocity and to all orders in the
running coupling constant of QCD. The decay rates for all four P states into
light hadronic or electromagnetic final states are expressed in terms of two
phenomenological parameters, whose coefficients are perturbatively calculable.
Logarithms of the binding energy encountered in previous perturbative
calculations of P-wave decays are factored into a phenomenological parameter
that is related to the probability for the heavy quark-antiquark pair to be in
a color-octet S-wave state. Applying these predictions to charmonium, we use
measured decay rates for the $\chione$ and $\chitwo$ to predict the decay rates
of the $\chizero$ and $h_c$.


title: Improved Nonrelativistic QCD for Heavy Quark Physics

abstract:
  We construct an improved version of nonrelativistic QCD for use in lattice
simulations of heavy quark physics, with the goal of reducing systematic errors
from all sources to below 10\%. We develop power counting rules to assess the
importance of the various operators in the action and compute all leading order
corrections required by relativity and finite lattice spacing. We discuss
radiative corrections to tree level coupling constants, presenting a procedure
that effectively resums the largest such corrections to all orders in
perturbation theory. Finally, we comment on the size of nonperturbative
contributions to the coupling constants.


title: Dynamics of Langevin Simulation

abstract:
  This chapter [of a supplement to Prog. Theo. Phys.] reviews numerical
simulations of quantum field theories based on stochastic quantization and the
Langevin equation. The topics discussed include renormalization of finite
step-size algorithms, Fourier acceleration, and the relation of the Langevin
equation to hybrid stochastic algorithms and hybrid Monte Carlo.


title: Ising Model Coupled to Three-Dimensional Quantum Gravity

abstract:
  We have performed Monte Carlo simulations of the Ising model coupled to
three-dimensional quantum gravity based on a summation over dynamical
triangulations. These were done both in the microcanonical ensemble, with the
number of points in the triangulation and the number of Ising spins fixed, and
in the grand canoncal ensemble. We have investigated the two possible cases of
the spins living on the vertices of the triangulation (``diect'' case) and the
spins living in the middle of the tetrahedra (``dual'' case). We observed phase
transitions which are probably second order, and found that the dual
implementation more effectively couples the spins to the quantum gravity.


title: The Running Coupling from Lattice Gauge Theory

abstract:
  From an accurate determination of the inter-quark potential, one can study
the running coupling constant for a range of $R$-values and hence estimate the
scale $\Lambda_{\msbar} $. Detailed results are presented for $SU(2)$ pure
gauge theory to illustrate the method.


title: Tunneling and Energy Splitting in Ising Models

abstract:
  The energy splitting $E_{0a}$ in two and four dimensional Ising models is
measured in a cylindrical geometry on finite lattices. By comparing to exact
results in the two dimensional Ising model we demonstrate that $E_{0a}$ can be
extracted very reliably from Monte Carlo calculations in practice. In four
dimensions we compare the measured $E_{0a}$ with two different theoretical
predictions on the finite size behavior of the energy splitting. We find that
our numerical data are in favor of the predictions based on the semiclassical
dilute instanton gas approximation.


title: Reflection positive formulation of chiral gauge theories on a lattice

abstract:
  Gauge invariant chiral theories satisfying the reflection positivity is
constructed on a lattice. This requires the introduction of "half gauge fields"
defined some time ago by Brydges, Fr\"{o}hlich, and Seiler \cite{BFS}. A
two-dimensional model is considered in some detail.


title: Effective Field Theories

abstract:
  Effective field theories encode the predictions of a quantum field theory at
low energy. The effective theory has a fairly low ultraviolet cutoff. As a
result, loop corrections are small, at least if the effective action contains a
term which is quadratic in the fields, and physical predictions can be read
straight from the effective Lagrangean.
  Methods will be discussed how to compute an effective low energy action from
a given fundamental action, either analytically or numerically, or by a
combination of both methods. Basically,the idea is to integrate out the high
frequency components of fields. This requires the choice of a "blockspin",i.e.
the specification of a low frequency field as a function of the fundamental
fields. These blockspins will be the fields of the effective field theory. The
blockspin need not be a field of the same type as one of the fundamental
fields, and it may be composite. Special features of blockspins in nonabelian
gauge theories will be discussed in some detail.
  In analytical work and in multigrid updating schemes one needs interpolation
kernels $\A$ from coarse to fine grid in addition to the averaging kernels $C$
which determines the blockspin. A neural net strategy for finding optimal
kernels is presented.
  Numerical methods are applicable to obtain actions of effective theories on
lattices of finite volume. The constraint effective potential) is of particular
interest. In a Higgs model it yields the free energy, considered as a function
of a gauge covariant magnetization. Its shape determines the phase structure of
the theory. Its loop expansion with and without gauge fields can be used to
determine finite size corrections to numerical data.


title:
The Quantized $O(1,2)/O(2)\times Z_2$ Sigma Model Has No Continuum Limit
  in Four Dimensions. I. Theoretical Framework

abstract:
  The nonlinear sigma model for which the field takes its values in the coset
space $O(1,2)/O(2)\times Z_2$ is similar to quantum gravity in being
perturbatively nonrenormalizable and having a noncompact curved configuration
space. It is therefore a good model for testing nonperturbative methods that
may be useful in quantum gravity, especially methods based on lattice field
theory. In this paper we develop the theoretical framework necessary for
recognizing and studying a consistent nonperturbative quantum field theory of
the $O(1,2)/O(2)\times Z_2$ model. We describe the action, the geometry of the
configuration space, the conserved Noether currents, and the current algebra,
and we construct a version of the Ward-Slavnov identity that makes it easy to
switch from a given field to a nonlinearly related one. Renormalization of the
model is defined via the effective action and via current algebra. The two
definitions are shown to be equivalent. In a companion paper we develop a
lattice formulation of the theory that is particularly well suited to the sigma
model, and we report the results of Monte Carlo simulations of this lattice
model. These simulations indicate that as the lattice cutoff is removed the
theory becomes that of a pair of massless free fields. Because the geometry and
symmetries of these fields differ from those of the original model we conclude
that a continuum limit of the $O(1,2)/O(2)\times Z_2$ model which preserves
these properties does not exist.


title: Chiral Limit of Nucleon Lattice Electromagnetic Form Factors

abstract:
  We calculate electric and magnetic form factors of protons and neutrons in
quenched Monte Carlo lattice QCD on a $16^3\times 24$ lattice at $\beta = 6.0$
using Wilson fermions. We employ a method which characterizes one of the
nucleon fields as a fixed zero-momentum secondary source. Extrapolating the
overall data set to the chiral limit, we find acceptable fits for either dipole
or monopole forms and extract proton and neutron magnetic moments, the
magnitude of which are $10$ to $15\%$ low compared to experiment. In the
extrapolation of the dipole fit of the form factors, we find that the dipole to
nucleon mass ratio is about $7\%$ low compared to experiment. In addition, we
obtain positive values of the neutron electric form factor, which, however, are
poorly represented by a popular phenomenological form at intermediate to small
$\kappa$ values. A zero-momentum technique for extracting hadron magnetic
moments is briefly discussed and shown to yield unrealistically small magnetic
moment values.


title:
Quenched Hadrons using Wilson and O(a)-Improved Fermion Actions at
  beta=6.2

abstract:
  We present the first study of the light hadron spectrum and decay constants
for quenched QCD using an O(a)-improved nearest-neighbour Wilson fermion action
at \beta=6.2. We compare the results with those obtained using the standard
Wilson fermion action, on the same set of 18 gauge field configurations of a
24^3 times 48 lattice. For pseudoscalar meson masses in the range 330-800 MeV,
we find no significant difference between the results for the two actions. The
scales obtained from the string tension and mesonic sector are consistent, but
differ from that derived from baryon masses. The ratio of the pseudoscalar
decay constant to the vector meson mass is roughly independent of quark mass as
observed experimentally, and in approximate agreement with the measured value.


title:
The Quantized $O(1,2)/O(2)\times Z_2$ Sigma Model Has No Continuum Limit
  in Four Dimensions. II. Lattice Simulation

abstract:
  A lattice formulation of the $O(1,2)/O(2)\times Z_2$ sigma model is
developed, based on the continuum theory presented in the preceding paper.
Special attention is given to choosing a lattice action (the ``geodesic''
action) that is appropriate for fields having noncompact curved configuration
spaces. A consistent continuum limit of the model exists only if the
renormalized scale constant $\beta_R$ vanishes for some value of the bare scale
constant~$\beta$. The geodesic action has a special form that allows direct
access to the small-$\beta$ limit. In this limit half of the degrees of freedom
can be integrated out exactly. The remaining degrees of freedom are those of a
compact model having a $\beta$-independent action which is noteworthy in being
unbounded from below yet yielding integrable averages. Both the exact action
and the $\beta$-independent action are used to obtain $\beta_R$ from Monte
Carlo computations of field-field averages (2-point functions) and
current-current averages. Many consistency cross-checks are performed. It is
found that there is no value of $\beta$ for which $\beta_R$ vanishes. This
means that as the lattice cutoff is removed the theory becomes that of a pair
of massless free fields. Because these fields have neither the geometry nor the
symmetries of the original model we conclude that the $O(1,2)/O(2)\times Z_2$
model has no continuum limit.


title: Simulated Tempering: A New Monte Carlo Scheme

abstract:
  We propose a new global optimization method ({\em Simulated Tempering}) for
simulating effectively a system with a rough free energy landscape (i.e. many
coexisting states) at finite non-zero temperature. This method is related to
simulated annealing, but here the temperature becomes a dynamic variable, and
the system is always kept at equilibrium. We analyze the method on the Random
Field Ising Model, and we find a dramatic improvement over conventional
Metropolis and cluster methods. We analyze and discuss the conditions under
which the method has optimal performances.


title: Critical mass in nonzero temperature QCD with staggered fermions

abstract:
  The behaviour of the chiral condensate in QCD is investigated by means of a
study of the distribution of the zeros of the partition function in the complex
quark mass plane. Simulations are performed at fixed temperature on three
different spatial volumes at $\beta=5.04$ and at $\beta=4.9$ and $\beta=5.2$ on
a $4^4$ lattice. Evidence is found for a chirally related transition at
non-zero quark mass in the intermediate coupling region for $\beta < 5.2 $ but
superimposed upon a smooth behaviour for the condensate. The critical mass at
which this transition is found is only weakly dependent on the spatial volume
and decreas with decreasing temperature.


title: Quenched Chiral Logarithms

abstract:
  I develop a diagrammatic method for calculating chiral logarithms in the
quenched approximation. While not rigorous, the method is based on physically
reasonable assumptions, which can be tested by numerical simulations. The main
results are that, at leading order in the chiral expansion, (a) there are no
chiral logarithms in quenched $f_\pi$, for $m_u=m_d$; (b) the chiral logarithms
in $B_K$ and related kaon B-parameters are, for $m_d=m_s$, the same in the
quenched approximation as in the full theory; (c) for $m_\pi$ and the
condensate, there are extra chiral logarithms due to loops containing the
$\eta'$, which lead to a peculiar non-analytic dependence of these quantities
on the bare quark mass. Following the work of Gasser and Leutwyler, I discuss
how there is a predictable finite volume dependence associated with each chiral
logarithm. I compare the resulting predictions with numerical results: for most
quantities the expected volume dependence is smaller than the errors, but for
$B_V$ and $B_A$ there is an observed dependence which is consistent with the
predictions.


title: 3d quantum gravity coupled to matter

abstract:
  We investigate the phase structure of three-dimensional quantum gravity
coupled to an Ising spin system by means of numerical simulations. The quantum
gravity part is modelled by the summation over random simplicial manifolds, and
the Ising spins are located in the center of the tetrahedra, which constitute
the building blocks of the piecewise linear manifold. We find that the coupling
between spin and geometry is weak away from the critical point of the Ising
model. At the critical point there is clear coupling, which however does not
seem to change the first order transition between the ``hot'' and ``cold''
phase of three dimensional simplicial quantum gravity observed earlier.


title: Parity breaking at high temperature and density

abstract:
  We investigate the question of parity breaking in three-dimensional Euclidean
SU(2) gauge-Higgs theory by Monte Carlo simulations. We observe no sign of
spontaneous parity breaking in the behaviour of both local and non-local gauge
invariant operators. However, the presence of parity odd terms in the action
can induce a phase transition to a parity odd ground state which is
characterized by a Chern-Simons like condensate. The implications for various
proposed scenarios of fermion number non-conservation is discussed.


title: Mirror fermions in chiral gauge theories

abstract:
  Mirror fermions appear naturally in lattice formulations of the standard
model. The phenomenological limits on their existence and discovery limits at
future colliders are discussed. After an introduction of lattice actions for
chiral Yukawa-models, a recent numerical simulation is presented. In
particular, the emerging phase structure and features of the allowed region in
renormalized couplings are discussed.


title: Grand Canonical Partition Function of a 2-dimensional Hubbard Model

abstract:
  We present a new technique for a numerical analysis of the phase structure of
the 2D Hubbard model as a function of the hole chemical potential. The grand
canonical partition function for the model is obtained via Monte Carlo
simulations. The dependence of the hole occupation number on the chemical
potential and the temperature is evaluated. These calculations, together with a
study of the Yang-Lee zeros of the grand canonical partition function, show
evidence of a phase transition at zero temperature and particle density below
half-filling. The binding energy of a pair of holes is calculated in the low
temperature regime and the possibility for pairing is explored.


title:
Regularizations, Anomalies and Fermion Number Non-Conservation in Chiral
  Gauge Theories

abstract:
  We study how fermion number conservation fails in fermion number preserving
regularization schemes. We show that the fermion number have to be carried by
the gauge field configurations with non-zero winding number in this scheme and
this fermion number is not conserved in the presence of instantons. We also
consider other types of regularization scheme which have different global
symmetries. In particular, we point out that the fermion number is conserved in
the lattice chiral gauge theories with the Wilson-Yukawa coupling.


title:
Central Charge of the Parallelogram Lattice Strong Coupling Schwinger
  Model

abstract:
  We put forth a Fierzed hopping expansion for strong coupling Wilson fermions.
As an application, we show that the strong coupling Schwinger model on
parallelogram lattices with nonbacktracking Wilson fermions span, as a function
of the lattice skewness angle, the $\Delta = -1$ critical line of $6$-vertex
models. This Fierzed formulation also applies to backtracking Wilson fermions,
which as we describe apparently correspond to richer systems. However, we have
not been able to identify them with exactly solved models.


title:
High-Temperature series for the $RP^{n-1}$ lattice spin model
  (generalized Maier-Saupe model of nematic liquid crystals) in two space
  dimensions and with general spin dimensionality n

abstract:
  High temperature series expansions of the spin-spin correlation functions of
the RP^{n-1} spin model on the square lattice are computed through order
beta^{8} for general spin dimensionality n. Tables are reported for the
expansion coefficients of the energy per site, the susceptibility and the
second correlation moment.


title:
Numerical Investigation of the Interface Tension in the
  three-dimensional Ising Model

abstract:
  The interface tension in the three-dimensional Ising model in the low
temperature phase is investigated by means of the Monte Carlo method. Together
with other physically relevant quantities it is obtained from a calculation of
time-slice correlation functions in a cylindrical geometry. The results at
three different values of the temperature are compared with the predictions
from a semiclassical approximation in the framework of renormalized $\phi^4$
theory in three dimensions, and are in good agreement with them.


title: Three Dimensional Quantum Gravity Coupled to Ising Matter

abstract:
  We establish the phase diagram of three--dimensional quantum gravity coupled
to Ising matter. We find that in the negative curvature phase of the quantum
gravity there is no disordered phase for ferromagnetic Ising matter because the
coordination number of the sites diverges. In the positive curvature phase of
the quantum gravity there is evidence for two spin phases with a first order
transition between them.


title:
Renormalization group and triviality in noncompact lattice QED with
  light fermions

abstract:
  In the framework of noncompact lattice QED with light fermions, we derive the
functional dependence of the average energy per plaquette on the bare
parameters using block-spin Renormalization Group arguments and assuming that
the renormalized coupling vanishes. Our numerical results for this quantity in
$8^4$ and $10^4$ lattices show evidence for triviality in the weak coupling
phase and point to a non vanishing value for the renormalized coupling constant
in the strong coupling phase.


title: Lattice QCD with 8 Light Quark Flavors

abstract:
  QCD with eight flavors is studied on $16^3\times N_t$ lattices with $N_t=4$,
6, 8, 16 and 32, a dynamical quark mass $ma=0.015$ and lattice coupling
$\beta=6/g^2$ between 4.5 and 5.0. For $N_t=16$ and 32, hadron masses and
screening lengths are computed for a variety of valence quark masses. The
previously observed, strong, first-order transition for $N_t=4$, 6 and 8 is
seen, for $N_t=16$, to become a $\beta$-independent, zero-temperature
transition characterized by a factor of $\approx 3$ change in lattice scale.
This strong, first-order transition restores chiral symmetry, at least for
$N_t=4$, 6 and 8, producing a chirally symmetric, weak-coupling phase. However,
as $N_t$ increases to 16, the chiral symmetry properties of the weak-coupling
side of the zero-temperature transition are unclear and offer a hint of a
normal, finite-temperature, chiral symmetry breaking transition in the
weak-coupling phase.


title: Exact Solution of Induced Lattice Gauge Theory at Large $N$

abstract:
  We find the exact solution of a recently proposed model of the lattice gauge
theory induced by heavy scalar field in adjoint representation at $ N= \infty $
for arbitrary dimension $D$. The nonlinear integral equation for the gauge
invariant density of eigenvalues of the vacuum average of the scalar field is
derived. In the continuum limit, the density grows as $ \phi^{\alpha} $ where $
\alpha = 1 + \frac{1}{\pi}\arccos\frac{D}{3D-2} $.


title: Finite size effects and scaling in lattice CP(N-1)

abstract:
  We present model predictions for the spectrum of $CP^{N-1}$ in a periodic box
and use them to interpret the strong finite size effects observed in lattice
simulations at medium values of $N$. The asymptotic scaling behaviour of
alternative lattice actions is discussed along with some aspects of multigrid
algorithm efficiency.


title: Resonance Scattering Phase Shifts in a 2-d Lattice Model

abstract:
  We study a simple 2-d model representing two fields with different mass and a
3-point coupling term. The phase shift in the resonating 2-particle channel is
determined from the energy spectrum obtained in Monte Carlo simulations on
finite lattices. Masses and wave function renormalization constants of the
fields as well as mass and width of the resonance are determined and discussed.
The representation of scattering states in terms of the considered operators is
analysed.


title:
Massless Decoupled Doublers: Chiral Yukawa Models and Chiral Gauge
  Theories

abstract:
  We present a new method for regularizing chiral theories on the lattice. The
arbitrariness in the regularization is used in order to decouple massless
replica fermions. A continuum limit with only one fermion is obtained in
perturbation theory and a Golterman-Petcher like symmetry related to the
decoupling of the replicas in the non-perturbative regime is identified. In the
case of Chiral Gauge Theories gauge invariance is broken at the level of the
regularization, so our approach shares many of the characteristics of the Rome
approach.


title: Gauge Fixing on the Lattice without Ambiguity

abstract:
  A new gauge fixing condition is discussed, which is (lattice) rotation
invariant, has the `smoothness' properties of the Landau gauge but can be
efficiently computed and is unambiguous for almost all lattice gauge field
configurations.


title: Virtual Bond Percolation for Ising Cluster Dynamics

abstract:
  The Fortuin-Kasteleyn mapping between the Ising model and the site-bond
correlated percolation model is shown to be only one of an infinite class of
exact mappings. These new cluster representations are a result of
"renormalized" percolation rules correlated to entire blocks of spins. For
example these rules allow for percolation on "virtual" bonds between spins not
present in the underlying Hamiltonian. As a consequence we can define new
random cluster theories each with its own Monte Carlo cluster dynamics that
exactly reproduce the Ising model. By tuning parameters on the critical
percolation surface, it is demonstrated numerically that cluster algorithms can
be formulated for the 2-d and 3-d Ising model that have smaller
autocorrelations than the original Swendsen-Wang algorithm.


title: Fermion-Higgs model with Reduced Staggered Fermions

abstract:
  We introduce a lattice fermion-Higgs model with one component `reduced
staggered' fermions. In order to use the fermion field as efficiently as
possible we couple the two {\em staggered} flavors to the O(4) Higgs field
leading to a model with only one SU(2) doublet in the scaling region. The
number of fermions is doubled in a numerical investigation of the model with
the hybrid Monte Carlo algorithm. We present results for the phase diagram,
particle masses and renormalized couplings on lattices ranging in size from
$6^3 24$ to $16^3 24$.


title: Hopping Parameter Expansion for Heavy-Light Systems

abstract:
  We present a technique which permits the calculation of two-point functions
of operators containing one heavy quark and an arbitrary number of light quarks
as analytic functions of the heavy-quark mass. It is based on the standard
Jacobi linear solver used for the calculation of quark propagators. Results for
the heavy-light pseudoscalar and vector meson masses are obtained on 16^3x48
lattices at beta = 6.2 using the Wilson fermion action, and agree with
published data. The incorporation of smeared operators and $O(a)$-improved
actions presents no problems.


title: Absence of Chiral Fermions in the Eichten--Preskill Model

abstract:
  The model proposed by Eichten and Preskill for obtaining theories with chiral
fermions from the lattice is shown to undergo spontaneous symmetry breaking. In
addition, the fermions appear to be Dirac-like everywhere in the phase diagram
with no room for undoubled Weyl fermions. The phase diagram of a closely
related Higgs-Yukawa model is similar to that of the Smit--Swift model, which
also does not give rise to chiral fermions. These results cast serious doubts
on the original scenario for the emergence of chiral fermions.


title: More about orbitally excited hadrons from lattice QCD

abstract:
  This is a second paper describing the calculation of spectroscopy for
orbitally excited states from lattice simulations of Quantum Chromodynamics.
New features include higher statistics for P-wave systems and first results for
the spectroscopy of D-wave mesons and baryons, for relatively heavy quark
masses. We parameterize the Coulomb gauge wave functions for P-wave and D-wave
systems and compare them to those of their corresponding S-wave states.


title: An Effective Model for Crumpling in Two Dimensions?

abstract:
  We investigate the crumpling transition for a dynamically triangulated random
surface embedded in two dimensions using an effective model in which the
disordering effect of the $X$ variables on the correlations of the normals is
replaced by a long-range ``antiferromagnetic'' term. We compare the results
from a Monte Carlo simulation with those obtained for the standard action which
retains the $X$'s and discuss the nature of the phase transition.


title: A Method for Simulating Chiral Fermions on the Lattice

abstract:
  A method for simulating chiral gauge theories on the lattice is proposed,
involving zeromodes on a topological defect. Lattice doublers may be decoupled
in a gauge invariant manner, and flavor anomalies can be directly observed on a
finite lattice. (Requires harvmac)


title: Chiral Fermions and Anomalies on a Finite Lattice

abstract:
  A recent proposal by Kaplan for a chiral gauge theory on the lattice is
tested with background gauge fields. The spectrum of the finite lattice
Hamiltonian is calculated and the existence of a chiral fermion is
demonstrated. Lattice doublers are found to decouple. The flavor anomalies,
which are in agreement with the continuum anomaly relation, are obeserved on a
finite lattice. Non-trivial anomaly cancellation is observed in a chiral gauge
current.


title: The XY Model Coupled to Two-Dimensional Quantum Gravity

abstract:
  We perform Monte Carlo simulations using the Wolff cluster algorithm of the
XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with
coupling to two-dimensional quantum gravity). We compare the numerical results
with the theoretical expectation that the phase transition remains of KT type
when the XY model is coupled to gravity. We also examine whether the
universality we discovered in our earlier work on various Potts models with the
same value of the central charge, $c$, carries over to the XY model, which has
$c=1$.


title: Numerical study of Yang-Mills classical solutions on the twisted torus

abstract:
  We use the lattice cooling method to investigate the structure of some gauge
fixed SU(2) Yang-Mills classical solutions of the euclidean equations of motion
which are defined in the 3-torus with symmetric twisted boundary conditions.


title: Tunneling and the Spectrum of the Potts Model

abstract:
  The three-dimensional, three-state Potts model is studied as a paradigm for
high temperature quantum chromodynamics. In a high statistics numerical
simulation using a Swendson-Wang algorithm, we study cubic lattices of
dimension as large as $64^3$ and measure correlation functions on long lattices
of dimension $20^2\times 120$ and $30^2\times 120$. These correlations are
controlled by the spectrum of the transfer matrix. This spectrum is studied in
the vicinity of the phase transition. The analysis classifies the spectral
levels according to an underlying $S_3$ symmetry. Near the phase transition the
spectrum agrees nicely with a simple four-component hamiltonian model. In the
context of this model, we find that low temperature ordered-ordered interfaces
nearly always involve a disordered phase intermediate. We present a new
spectral method for determining the surface tension between phases.


title:
Spectroscopy, Scaling and Critical Indices in Strongly Coupled Quenched
  QED

abstract:
  The interplay of spectroscopy, scaling laws and critical indices is studied
in strongly coupled quenched QED. Interpreted as a model of technicolor having
strong interactions at short distances, we predict the techni-meson mass
spectrum in a simplified model of a dynamically generated top quark mass $M_f$.
Our results support the strict inequality that the techni-sigma mass $M_\sigma$
is less than twice the dynamical quark mass $M_f$, and confirm that the
techni-pion is a Nambu-Goldstone boson. The level ordering $0 = M_\pi <
M_\sigma < 2M_f < M_\rho < M_{a1} $ is found.An equation of state, and scaling
laws are derived for the techni-meson masses by exploiting correlation length
scaling. The resulting universality relations are confirmed by simulations on
$16^4$, $32\times 16^3$ and $32^4$ lattices. The anomalous dimension $\eta$ is
measured to be approximatively $0.50$ in good agreement with past lattice
simulations and hyperscaling relations, as well as with the analytic solution
of the quenched, planar gauged Nambu-Jona Lasinio model solved by continuum
Schwinger-Dyson equation techniques.


title:
London relation and fluxoid quantization for monopole currents in U(1)
  lattice gauge theory

abstract:
  We explore the analogy between quark confinement and the Meissner effect in
superconductors. We measure the response of color-magnetic "supercurrents" from
Dirac magnetic monopoles to the presence of a static quark-antiquark pair in
four dimensional U(1) lattice gauge theory. Our results indicate that in the
confined phase these currents screen the color-electric flux due to the quarks
in an electric analogy of the Meisner effect. We show that U(1) lattice guage
theory obeys both a dual London equation and an electric fluxoid quantization
condition.


title: Low temperature expansion for the 3-d Ising Model

abstract:
  We compute the weak coupling expansion for the energy of the three
dimensional Ising model through 48 excited bonds. We also compute the
magnetization through 40 excited bonds. This was achieved via a recursive
enumeration of states of fixed energy on a set of finite lattices. We use a
linear combination of lattices with a generalization of helical boundary
conditions to eliminate finite volume effects.


title: Numerical Study of c>1 Matter Coupled to Quantum Gravity

abstract:
  We present the results of a numerical simulation aimed at understanding the
nature of the `c = 1 barrier' in two dimensional quantum gravity. We study
multiple Ising models living on dynamical $\phi^3$ graphs and analyse the
behaviour of moments of the graph loop distribution. We notice a universality
at work as the average properties of typical graphs from the ensemble are
determined only by the central charge. We further argue that the qualitative
nature of these results can be understood from considering the effect of
fluctuations about a mean field solution in the Ising sector.


title: Properties of Interfaces in the two and three dimensional Ising Model

abstract:
  To investigate order-order interfaces, we perform multimagnetical Monte Carlo
simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the
interfacial free energy from the infinite volume limit of the magnetic
probability density. Stringent tests of the numerical methods are performed by
reproducing with high precision exact $2D$ results. In the physically more
interesting $3D$ case we estimate the amplitude $F^s_0$ of the critical
interfacial tension $F^s = F^s_0 t^\mu$ to be $F^s_0 = 1.52 \pm 0.05$. This
result is in good agreement with a previous MC calculation by Mon, as well as
with experimental results for related amplitude ratios. In addition, we study
in some details the shape of the magnetic probability density for temperatures
below the Curie point.


title: Lattice QCD Spectroscopy with an Improved Wilson Fermion Action

abstract:
  We study the hadronic spectrum in quenched lattice QCD using an improved
Wilson fermion action (Hamber-Wu(1983),Eguchi-Kawamoto(1984)) at $\beta= 5.7$
and $\beta =6.0$. We find a systematic reduction of the finite spacing effects
compared to the results obtained by using the standard Wilson action.


title:
The Four-Fermi Model in Three Dimensions at Non-Zero Density and
  Temperature

abstract:
  The Four Fermi model with discrete chiral symmetry is studied in three
dimensions at non-zero chemical potential and temperature using the Hybrid
Monte Carlo algorithm. The number of fermion flavors is chosen large $(N_f=12)$
to compare with analytic results. A first order chiral symmetry restoring
transition is found at zero temperature with a critical chemical potential
$\mu_c$ in good agreement with the large $N_f$ calculations. The critical index
$\nu$ of the correlation length is measured in good agreement with analytic
calculations. The two dimensional phase diagram (chemical potential vs.
temperature) is mapped out quantitatively. Finite size effects on relatively
small lattices and non-zero fermion mass effects are seen to smooth out the
chiral transition dramatically.


title:
Scaling analysis of the O(4)-symmetric $\Phi^4$-theory in the broken
  phase

abstract:
  We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the
broken phase using the standard and a Symanzik improved action with infinite
bare self-coupling $\lambda$. A high precision Monte Carlo simulation is
performed by applying the reflection cluster algorithm. Employing the histogram
method we analytically continue to a sequence of values of the hopping
parameter $\kappa$ neighbouring the actually simulated ones. In the
investigated vicinity of the critical point $\kappa_{c}$ finite volume effects
affecting, e.g., the determination of the field expectation value $\Sigma$ and
the mass $m_\sigma$ of the $\sigma$-particle are very well described by 1-loop
renormalized perturbation theory. We carry out a detailed scaling analysis on a
high level of precision. Finally we discuss the upper bound on the Higgs mass
for both kinds of actions.


title:
The Universlity Class of Monopole Condensation in Non-Compact, Quenched
  Lattice QED

abstract:
  Finite size scaling studies of monopole condensation in noncompact quenched
lattice $QED$ indicate an authentic second order phase transition lying in the
universality class of four dimensional percolation. Since the upper critical
dimension of percolation is six, the measured critical indices are far from
mean-field values. We propose a simple set of ratios as the exact critical
indices for this transition. The implication of these results for critical
points in Abelian gauge theories are discussed.


title: Numerical Analysis of the Quark Fraction of the Proton Spin

abstract:
  We report on a lattice QCD estimate of the quark spin fraction of the proton
spin. The estimate is arrived at by means of a lattice QCD simulation of the
polarized proton matrix element of the Adler-Bell-Jackiw anomaly. The
preliminary result of the simulation is that this fraction is rather small.
This is in accord with the interpretation of the EMC experiment that the quark
spins are responsible for very little, if any, of the proton spin. (Talk given
at the Adriatico Research Conference on Polarization Dynamics in Nuclear and
Particle Physics, Trieste, January, 1992) NOTE: This paper is available only in
postscript form.


title: The Effective String of 3D Z_2 Gauge Theory as a c=1 compactified CFT

abstract:
  We report on a high precision Montecarlo test of the three dimensional Ising
gauge model at finite temperature. The string tension $\sigma$ is extracted
from the expectation values of correlations of Polyakov lines. Agreement with
the string tension extracted from Wilson loops is found only if the quantum
fluctuations of the flux tube are properly taken into account. The central
charge of the underlying conformal field theory is c=1.


title:
Gauge Dependence of Effective Quark Mass and Matrix Elements in
  Gaugefixed Large $N$ Strong Coupling Lattice QCD

abstract:
  In conjunction with recent numerical \hbox{$\lambda~\partial_0 A_0 +
\nabla\cdot\vec{A} =0$} ``$\lambda$-gauge'' results reported in a companion
paper, we construct an $N\to\infty$ Wilson loop picture of
$\lambda$-gaugefixing in which (I)the $\lambda$-gauge expectation value of a
link chain $C$ is the weighted sum over Wilson loops made by joining to $C$ all
selfavoiding chains $\widetilde{C}$ closing $C$. (II)Weights
$A_{\widetilde{C}}$, containing all the $\lambda$-dependence, are given by the
$\beta=0$ $\lambda$-gauge expectation value of $\widetilde{C}$.
(III)$A_{\widetilde{C}}$ equals path-products of coefficients from the trace
expansion of the gaugefixing Boltzmann weight. From (II) and (III) we deduce
formulas for $\beta =0$ quark matrix elements. We find that $M_q^{(\lambda)}$
decreases with increasing $\lambda$; the quark propagator dispersion relation
is not covariant when $\lambda\ne 1$; and $\Delta I=1/2$ matching coefficients
are $\lambda$-independent. These strong coupling features are qualitatively
consistent with numerical $\beta=5.7$ and $6.0$ results briefly described here
for comparison purposes but mainly presented in a companion paper.


title: Kinematics of Multigrid Monte Carlo

abstract:
  We study the kinematics of multigrid Monte Carlo algorithms by means of
acceptance rates for nonlocal Metropolis update proposals. An approximation
formula for acceptance rates is derived. We present a comparison of different
coarse-to-fine interpolation schemes in free field theory, where the formula is
exact. The predictions of the approximation formula for several interacting
models are well confirmed by Monte Carlo simulations. The following rule is
found: For a critical model with fundamental Hamiltonian H(phi), absence of
critical slowing down can only be expected if the expansion of <H(phi + psi)>
in terms of the shift psi contains no relevant (mass) term. We also introduce a
multigrid update procedure for nonabelian lattice gauge theory and study the
acceptance rates for gauge group SU(2) in four dimensions.


title: Fermions in Models with Wilson--Yukawa Couplings

abstract:
  Our work on models with Wilson--Yukawa couplings is reviewed. Conclusions
include the failure of such models to produce continuum chiral gauge theories.


title: On the Eichten--Preskill Proposal for Lattice Chiral Gauge Theories

abstract:
  We have studied the Eichten--Preskill proposal for constructing lattice
chiral gauge theories using both strong and weak coupling methods. The results
indicate that this proposal is unlikely to work due to a dynamical behavior
similar to that of the Smit--Swift proposal, which also does not give rise to
chiral fermions.


title: The Phase Diagram of a U(1) Higgs-Yukawa Model at Finite $\lambda$

abstract:
  In this paper we investigate how the phase diagram of a U(1) symmetric
Higgs-Yukawa system depends on the scalar self coupling $\lambda$. The phase
diagram of similar models with continuous symmetry were extensively studied in
the infinite scalar self coupling $\lambda=\infty$ limit. Recent analytical and
numerical calculations at zero self coupling showed qualitatively different
phase diagram, raising the question of the $\lambda$ dependence of the phase
diagram. Here we use analytical (large $N_f$, perturbative and mean field)
approximations as well as numerical simulations to investigate the system.


title: Recent Results of Multimagnetical Simulations of the Ising Model

abstract:
  To investigate order-order interfaces, we perform multimagnetical Monte Carlo
simulations of the $2D$ and $3D$ Ising model. Stringent tests of the numerical
methods are performed by reproducing with high precision exact $2D$ results. In
the physically more interesting $3D$ case we estimate the amplitude $F^s_0$ of
the critical interfacial tension.


title: The Theory of Dynamical Random Surfaces with Extrinsic Curvature

abstract:
  We analyze numerically the critical properties of a two-dimensional
discretized random surface with extrinsic curvature embedded in a
three-dimensional space. The use of the toroidal topology enables us to enforce
the non-zero external extension without the necessity of defining a boundary
and allows us to measure directly the string tension. We show that a phase
transition from the crumpled phase to the smooth phase observed earlier for a
spherical topology appears also for a toroidal surface for the same finite
value of the coupling constant of the extrinsic curvature term. The phase
transition is characterized by the vanishing of the string tension. We discuss
the possible non-trivial continuum limit of the theory, when approaching the
critical point. Numerically we find a value of the critical exponent $\n$ to be
between .38 and .42. The specific heat, related to the extrinsic curvature term
seems not to diverge (or diverge slower than logarithmically) at the critical
point.


title:
The Schr\"odinger Functional - a Renormalizable Probe for Non-Abelian
  Gauge Theories

abstract:
  Following Symanzik we argue that the Schr\"odinger functional in lattice
gauge theories without matter fields has a well-defined continuum limit. Due to
gauge invariance no extra counter terms are required. The Schr\"odinger
functional is, moreover, accessible to numerical simulations. It may hence be
used to study the scaling properties of the theory and in particular the
evolution of the renormalized gauge coupling from low to high energies. A
concrete proposition along this line is made and the necessary perturbative
analysis of the Schr\"odinger functional is carried through to 1-loop order.


title: Computation of the Running Coupling in the SU(2) Yang-Mills Theory

abstract:
  A finite-size scaling technique is applied to the SU(2) gauge theory (without
matter fields) to compute a non-perturbatively defined running coupling
alpha(q) for a range of momenta q given in units of the string tension K. We
find that already at rather low q, the evolution of alpha(q) is well described
by the 2-loop approximation to the Callan-Symanzik beta-function. At the
highest momentum reached, q=20 sqrt(K), we obtain alpha_MSbar(q)=0.187 +/-
0.005 +/- 0.009 for the running coupling in the MSbar scheme of dimensional
regularization.


title: On Heteropolymer Shape Dynamics

abstract:
  We investigate the time evolution of the heteropolymer model introduced by
Iori, Marinari and Parisi to describe some of the features of protein folding
mechanisms. We study how the (folded) shape of the chain evolves in time. We
find that for short times the mean square distance (squared) between chain
configurations evolves according to a power law, $D \sim t ^\nu$. We discuss
the influence of the quenched disorder (represented by the randomness of the
coupling constants in the Lennard-Jones potential) on value of the critical
exponent. We find that $\nu$ decreases from $\frac{2}{3}$ to $\frac{1}{2}$ when
the strength of the quenched disorder increases.


title: A Proposal for Simulating Chiral Fermions

abstract:
  We describe a method for evaluating chiral gauge theories that is not plagued
by the doubling problem. To demonstrate the efficiency of the approach, we
apply our ideas to the chiral Schwinger model.


title:
The Topological Susceptibility of the Lattice CP(n-1) Model on the Torus
  and the Sphere

abstract:
  The topological vacuum structure of the two-dimensional $~CP^{n-1}~$ model
for $~n = 3,5,7~$ is studied on the lattice. In particular we investigate the
small-volume limit on the torus as well as on the sphere and compare with
continuum results. For $~n \ge 5~$ , where lattice artifacts should be
suppressed, the topological susceptibility shows unexpectedly strong deviations
from asymptotic scaling. On the other hand there is an indication for a
convergence to values obtained analytically within the limit $~n \rightarrow
\infty~$ .


title: Lattice Charge Overlap: Towards the Elastic Limit

abstract:
  A numerical investigation of time-separated charge overlap measurements is
carried out for the pion in the context of lattice QCD using smeared Wilson
fermions. The evolution of the charge distribution function is examined and the
expected asymptotic time behavior $\sim e^{-(E_{q}-m_{\pi})t}$, where $t$
represents the charge density relative time separation, is clearly visible in
the Fourier transform. Values of the pion form factor are extracted using
point-to-smeared correlation functions and are seen to be consistent with the
expected monopole form from vector dominance. The implications of these results
for hadron structure calculations is briefly discussed.


title: 1/N Expansion and Particle Spectrum in Induced QCD

abstract:
  We study the 1/N expansion in the recently proposed model of the lattice
gauge theory induced by heavy scalar field in adjoint representation. In the
first approximation the fluctuations of the density of eigenvalues of the
scalar field are Gaussian, so that the scalar glueball spectrum is defined from
the corresponding linear wave equation.


title:
Improving Multigrid and Conventional Relaxation Algorithms for
  Propagators

abstract:
  Practical modifications of deterministic multigrid and conventional
relaxation algorithms are discussed. New parameters need not be tuned but are
determined by the algorithms themselves. One modification can be thought of as
``updating on a last layer consisting of a single site''. It eliminates
critical slowing down in computations of bosonic and fermionic propagators in a
fixed volume. Here critical slowing down means divergence of asymptotic
relaxation times as the propagators approach criticality. A remaining volume
dependence is weak enough in case of bosons so that conjugate gradient can be
outperformed. However, no answer can be given yet if the same is true for
staggered fermions on lattices of realizable sizes. Numerical results are
presented for propagators of bosons and of staggered fermions in 4-dimensional
$SU(2)$ gauge fields.


title:
The equivalence of the SU(N) Yang Mills Theory with a Purely Fermionic
  Model

abstract:
  We investigate the detailed conditions under which a purely fermionic model
with current-current interaction goes over to a renormalizable, asymptotically
free SU$(N)$ gauge theory.


title:
Fermion Interactions in the Wilson Yukawa Approach for Lattice Chiral
  Gauge Theories

abstract:
  We consider fermion-gauge couplings in the Wilson-Yukawa approach for lattice
chiral gauge theories. At the leading order of a fermionic hopping parameter
expansion we find that the fermion-gauge coupling has a chiral and tree-like
structure. We argue that this fermion-gauge coupling remains non-zero in the
continuum limit taken in the Higgs phase. Possible fermion-scalar couplings in
this approach are considered. We also evaluate the fermion interaction with an
external gauge field in the slightly modified model and show that it has a
chiral structure in general.


title: High Precision Verification of the Kosterlitz Thouless Scenario

abstract:
  We verify the Kosterlitz Thouless scenario for three different SOS
(solid-on-solid) models, including the dual transforms of XY-models with
Villain and with cosine action. The method is based on a matching of the
renormalization group (RG) flow of the candidate models with the flow of a bona
fide KT model, the exactly solvable BCSOS model. We obtain high precision
estimates for the critical couplings and other non-universal quantities.


title: Topography of the hot sphaleron Transitions

abstract:
  By numerical simulations in {\it real time} we provide evidence in favour of
sphaleron like transitions in the hot, symmetric phase of the electroweak
theory. Earlier performed observations of a change in the Chern-Simons number
are supplemented with a measurement of the lowest eigenvalues of the
three-dimensional staggered fermion Dirac operator and observations of the
spatial extension of energy lumps associated with the transition. The
observations corroborate on the interpretation of the change in Chern-Simons
numbers as representing continuum physics, not lattice artifacts. By combining
the various observations it is possible to follow in considerable detail the
time-history of thermal fluctuations of the classical gauge-field
configurations responsible for the change in the Chern-Simons number.


title:
Numerical simulation of heavy fermions in an SU(2)_L x SU(2)_R symmetric
  Yukawa model

abstract:
  An exploratory numerical study of the influence of heavy fermion doublets on
the mass of the Higgs boson is performed in the decoupling limit of a chiral
$\rm SU(2)_L \otimes SU(2)_R$ symmetric Yukawa model with mirror fermions. The
behaviour of fermion and boson masses is investigated at infinite bare quartic
coupling on $4^3 \cdot 8$, $6^3 \cdot 12$ and $8^3 \cdot 16$ lattices. A first
estimate of the upper bound on the renormalized quartic coupling as a function
of the renormalized Yukawa-coupling is given.


title: Crossover Between Weakly and Strongly Self-avoiding Random Surfaces

abstract:
  We investigate the crossover between weak and strong self-avoidance in a
simulation of random surfaces with extrinsic curvature. We consider both
dynamically triangulated and rigid surfaces with the two possible
discretizations of the extrinsic curvature term.


title: Multicanonical Spin Glass Simulations

abstract:
  We report a Monte Carlo simulation of the $2D$ Edwards-Anderson spin glass
model within the recently introduced multicanonical ensemble. Replica on
lattices of size $L^2$ up to $L=48$ are investigated. Once a true groundstate
is found, we are able to give a lower bound on the number of statistically
independent groundstates sampled. Temperature dependence of the energy, entropy
and other quantities of interest are easily calculable. In particular we report
the groundstate results. Computations involving the spin glass order parameter
are more tedious. Our data indicate that the large $L$ increase of the
ergodicity time is reduced to an approximately $V^3$ power law. Altogether the
results suggest that the multicanonical ensemble improves the situation of
simulations for spin glasses and other systems which have to cope with similar
problems of conflicting constraints.