34 research outputs found
Computation of the string tension in three dimensional Yang-Mills theory using large N reduction
We numerically compute the string tension in the large N limit of three
dimensional Yang-Mills theory using Wilson loops. Space-time loops are formed
as products of smeared space-like links and unsmeared time-like links. We use
continuum reduction and both unfolded and folded Wilson loops in the analysis.Comment: 13 pages, 10 figures, 2 tables, minor changes to the tex
Topology and Chiral Symmetry in QCD with Overlap Fermions
We briefly review the overlap formalism for chiral gauge theories, the
overlap Dirac operator for massless fermions and its connection to domain wall
fermions. We describe properties of the overlap Dirac operator, and methods to
implement it numerically. Finally, we give some examples of quenched
calculations of chiral symmetry breaking and topology with overlap fermions.Comment: 12 pages with 6 ps figures; crckapb.sty included; to appear in the
proceedings of the workshop "Lattice Fermions and Structure of the Vacuum",
Oct 5-9, Dubna, Russi
The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory
We study the random walk representation of the two-point function in
statistical mechanics models near the critical point. Using standard scaling
arguments we show that the critical exponent describing the vanishing of
the physical mass at the critical point is equal to . is
the Hausdorff dimension of the walk. is the exponent describing
the vanishing of the energy per unit length of the walk at the critical point.
For the case of O(N) models, we show that , where
is the crossover exponent known in the context of field theory. This implies
that the Hausdorff dimension of the walk is for O(N) models.Comment: 11 pages (plain TeX
Absence of Physical Walls in Hot Gauge Theories
This paper shows that there are no {\em physical} walls in the deconfined,
high-temperature phase of lattice gauge theory. In a Hamiltonian
formulation, the interface in the Wilson lines is not physical. The line
interface and its energy are interpreted in terms of physical variables. They
are associated with a difference between two partition functions. One includes
only the configurations with even flux across the interface. The other is
restricted to odd flux. Also, with matter present, there is no physical
metastable state. However, the free energy is lowered by the matter. This
effect is described in terms of physical variables.Comment: 25 pages, Revte
Topology and chiral symmetry in finite temperature QCD
We investigate the realization of chiral symmetry in the vicinity of the
deconfinement transition in quenched QCD using overlap fermions. Via the index
theorem obeyed by the overlap fermions, we gain insight into the behavior of
topology at finite temperature. We find small eigenvalues, clearly separated
from the bulk of the eigenvalues, and study the properties of their
distribution. We compare the distribution with a model of a dilute gas of
instantons and anti-instantons and find good agreement.Comment: 3 pages with 3 ps figures; to appear in the proceedings of Lattice
'99, Pisa, Italy, June 29 -- July 3, 1999. LATTICE99(topology
Critical Exponent for the Density of Percolating Flux
This paper is a study of some of the critical properties of a simple model
for flux. The model is motivated by gauge theory and is equivalent to the Ising
model in three dimensions. The phase with condensed flux is studied. This is
the ordered phase of the Ising model and the high temperature, deconfined phase
of the gauge theory. The flux picture will be used in this phase. Near the
transition, the density is low enough so that flux variables remain useful.
There is a finite density of finite flux clusters on both sides of the phase
transition. In the deconfined phase, there is also an infinite, percolating
network of flux with a density that vanishes as . On
both sides of the critical point, the nonanalyticity in the total flux density
is characterized by the exponent . The main result of this paper is
a calculation of the critical exponent for the percolating network. The
exponent for the density of the percolating cluster is . The specific heat exponent and the crossover exponent
can be computed in the -expansion. Since , the variation in the separate densities is much more rapid than
that of the total. Flux is moving from the infinite cluster to the finite
clusters much more rapidly than the total density is decreasing.Comment: 20 pages, no figures, Latex/Revtex 3, UCD-93-2