59 research outputs found
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
Adjoint Wilson Line in SU(2) Lattice Gauge Theory
The behavior of the adjoint Wilson line in finite-temperature, ,
lattice gauge theory is discussed. The expectation value of the line and the
associated excess free energy reveal the response of the finite-temperature
gauge field to the presence of an adjoint source. The value of the adjoint line
at the critical point of the deconfining phase transition is highlighted. This
is not calculable in weak or strong coupling. It receives contributions from
all scales and is nonanalytic at the critical point. We determine the general
form of the free energy. It includes a linearly divergent term that is
perturbative in the bare coupling and a finite, nonperturbative piece. We use a
simple flux tube model to estimate the value of the nonperturbative piece. This
provides the normalization needed to estimate the behavior of the line as one
moves along the critical curve into the weak coupling region.Comment: 21 pages, no figures, Latex/Revtex 3, UCD-93-1
Quark Confinement in C-periodic Cylinders at Temperatures above T_c
Due to the Gauss law, a single quark cannot exist in a periodic volume, while
it can exist with C-periodic boundary conditions. In a C-periodic cylinder of
cross section A = L_x L_y and length L_z >> L_x, L_y containing deconfined
gluons, regions of different high temperature Z(3) phases are aligned along the
z-direction, separated by deconfined- deconfined interfaces. In this geometry,
the free energy of a single static quark diverges in proportion to L_z. Hence,
paradoxically, the quark is confined, although the temperature T is larger than
T_c. At T around T_c, the confined phase coexists with the three deconfined
phases. The deconfined-deconfined interfaces can be completely or incompletely
wet by the confined phase. The free energy of a quark behaves differently in
these two cases. In contrast to claims in the literature, our results imply
that deconfined-deconfined interfaces are not Euclidean artifacts, but have
observable consequences in a system of hot gluons.Comment: 8 pages, Latex, no figure
Induced Universal Properties and Deconfinement
We propose a general strategy to determine universal properties induced by a
nearby phase transition on a non-order parameter field. A general
renormalizable Lagrangian is used, which contains the order parameter and a
non-order parameter field, and respects all the symmetries present. We
investigate the case in which the order parameter field depends only on space
coordinates and the case in which this field is also time dependent. We find
that the spatial correlators of the non-order parameter field, in both cases,
are infrared dominated and can be used to determine properties of the phase
transition. We predict a universal behavior for the screening mass of a generic
singlet field, and show how to extract relevant information from such a
quantity. We also demonstrate that the pole mass of the non-order parameter
field is not infrared sensitive. Our results can be applied to any continuous
phase transition. As an example we consider the deconfining transition in pure
Yang-Mills theory, and show that our findings are supported by lattice data.
Our analysis suggests that monitoring the spatial correlators of different
hadron species, more specifically the derivatives of these, provides an
efficient and sufficient way to experimentally uncover the deconfining phase
transition and its features.Comment: Added computational details and improved the text. The results are
unchange
Large-N spacetime reduction and the sign and silver-blaze problems of dense QCD
We study the spacetime-reduced (Eguchi-Kawai) version of large-N QCD with
nonzero chemical potential. We explore a method to suppress the sign
fluctuations of the Dirac determinant in the hadronic phase; the method employs
a re-summation of gauge configurations that are related to each other by center
transformations. We numerically test this method in two dimensions, and find
that it successfully solves the silver-blaze problem. We analyze the system
further, and measure its free energy F, the average phase theta of its Dirac
determinant, and its chiral condensate . We show that F and
are independent of mu in the hadronic phase but that, as chiral
perturbation theory predicts, the quenched chiral condensate drops from its
mu=0 value when mu~(pion mass)/2. Finally, we find that the distribution of
theta qualitatively agrees with further, more recent, predictions from chiral
perturbation theory.Comment: 43 pages, 17 figure
Schwinger Model Green functions with topological effects
The fermion propagator and the 4-fermion Green function in the massless QED2
are explicitly found with topological effects taken into account. The
corrections due to instanton sectors k=+1,-1, contributing to the propagator,
are shown to be just the homogenous terms admitted by the Dyson-Schwinger
equation for S. In the case of the 4-fermion function also sectors k=+2,-2 are
included into consideration. The quark condensates are then calculated and are
shown to satisfy cluster property. The theta-dependence exhibited by the Green
functions corresponds to and may be removed by performing certain chiral gauge
transformation.Comment: 16 pages, in REVTE
Level Crossing for Hot Sphalerons
We study the spectrum of the Dirac Hamiltonian in the presence of high
temperature sphaleron-like fluctuations of the electroweak gauge and Higgs
fields, relevant for the conditions prevailing in the early universe. The
fluctuations are created by numerical lattice simulations. It is shown that a
change in Chern-Simons number by one unit is accompanied by eigenvalues
crossing zero and a change of sign of the generalized chirality \tGf=
(-1)^{2T+1} \gf which labels these modes. This provides further evidence that
the sphaleron-like configurations observed in lattice simulations may be viewed
as representing continuum configurations.Comment: Latex file, 29 pages + 13 figure
Domain walls and perturbation theory in high temperature gauge theory: SU(2) in 2+1 dimensions
We study the detailed properties of Z_2 domain walls in the deconfined high
temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both
by computer simulations of the lattice theory and by one-loop perturbative
calculations. The latter are carried out both in the continuum and on the
lattice. We find that leading order perturbation theory reproduces the detailed
properties of these domain walls remarkably accurately even at temperatures
where the effective dimensionless expansion parameter, g^2/T, is close to
unity. The quantities studied include the surface tension, the action density
profiles, roughening and the electric screening mass. It is only for the last
quantity that we find an exception to the precocious success of perturbation
theory. All this shows that, despite the presence of infrared divergences at
higher orders, high-T perturbation theory can be an accurate calculational
tool.Comment: 75 pages, LaTeX, 14 figure
A Study of the 't Hooft Model with the Overlap Dirac Operator
We present the results of an exploratory numerical study of two dimensional
QCD with overlap fermions. We have performed extensive simulations for U(N_c)
and SU(N_c) color groups with N_c=2, 3, 4 and coupling constants chosen to
satisfy the 't Hooft condition g^2 N_c =const=4/3. We have computed the meson
spectrum and decay constants, the topological susceptibility and the chiral
condensate. For U(N_c) gauge groups, our results indicate that the
Witten-Veneziano relation is satisfied within our statistical errors and that
the chiral condensate for N_f=1 is compatible with a non-zero value. Our
results exhibit universality in N_c and confirm once more the excellent chiral
properties of the overlap-Dirac operator.Comment: 18 pages, 4 figure
The search for ``polarized'' instantons in the vacuum
The new phase of a gauge theory in which the instantons are ``polarized'',
i.e. have the preferred orientation is discussed. A class of gauge theories
with the specific condensates of the scalar fields is considered. In these
models there exists an interaction between instantons resulting from
one-fermion loop correction. The interaction makes the identical orientation of
instantons to be the most probable, permitting one to expect the system to
undergo the phase transition into the state with polarized instantons. The
existence of this phase is confirmed in the mean-field approximation in which
there is the first order phase transition separating the ``polarized phase''
from the usual non-polarized one. The considered phase can be important for the
description of gravity in the framework of the gauge field theory.Comment: 16 pages, 2 Postscript figure
- …