185 research outputs found
Block Spin Effective Action for Polyakov Loops in 4D SU(2) LGT
Using a variant of the IMCRG method of Gupta and Cordery, we explicitly
compute majority rule block spin effective actions for the signs of the
Polyakov loops in 4D SU(2) finite temperature lattice gauge theories. To the
best of our knowledge, this is the first attempt to compute numerically
effective actions for the Polyakov loop degrees of freedom in 4D SU(2). The
most important observations are: 1. The renormalization group flow at the
deconfinement transition can be nicely matched with the flow of the 3D Ising
model, thus confirming the Svetitsky-Yaffe conjecture. 2. The IMCRG simulations
of the FT SU(2) model have strongly reduced critical slowing down.Comment: Contribution to the Lattice 97 proceedings, LaTeX, 3 pages, 3
figures, uses espcrc2.sty, epsfig.st
Effective actions for finite temperature Lattice Gauge Theories
We consider a lattice gauge theory at finite temperature in (+1)
dimensions with the Wilson action and different couplings and
for timelike and spacelike plaquettes. By using the character
expansion and Schwinger-Dyson type equations we construct, order by order in
, an effective action for the Polyakov loops which is exact to all
orders in . As an example we construct the first non-trivial order in
for the (3+1) dimensional SU(2) model and use this effective action
to extract the deconfinement temperature of the model.Comment: Talk presented at LATTICE96(finite temperature
Percolation and Critical Behaviour in SU(2) Gauge Theory
The paramagnetic-ferromagnetic transition in the Ising model can be described
as percolation of suitably defined clusters. We have tried to extend such
picture to the confinement-deconfinement transition of SU(2) pure gauge theory,
which is in the same universality class of the Ising model. The cluster
definition is derived by approximating SU(2) by means of Ising-like effective
theories. The geometrical transition of such clusters turns out to describe
successfully the thermal counterpart for two different lattice regularizations
of (3+1)-d SU(2).Comment: Lattice 2000 (Finite Temperature), 4 pages, 4 figures, 2 table
Cluster Percolation and Explicit Symmetry Breaking in Spin Models
Many features of spin models can be interpreted in geometrical terms by means
of the properties of well defined clusters of spins. In case of spontaneous
symmetry breaking, the phase transition of models like the q-state Potts model,
O(n), etc., can be equivalently described as a percolation transition of
clusters. We study here the behaviour of such clusters when the presence of an
external field H breaks explicitly the global symmetry of the Hamiltonian of
the theory. We find that these clusters have still some interesting
relationships with thermal features of the model.Comment: Proceedings of Lattice 2001 (Berlin), 3 pages, 3 figure
Breakdown of staggered fermions at nonzero chemical potential
The staggered fermion determinant is complex when the quark chemical
potential mu is nonzero. Its fourth root, used in simulations with dynamical
fermions, will have phase ambiguities that become acute when Re mu is
sufficiently large. We show how to resolve these ambiguities, but our
prescription only works very close to the continuum limit. We argue that this
regime is far from current capabilities. Other procedures require being even
closer to the continuum limit, or fail altogether, because of unphysical
discontinuities in the measure. At zero temperature the breakdown is expected
when Re mu is greater than approximately half the pion mass. Estimates of the
location of the breakdown at nonzero temperature are less certain.Comment: 6 pages RevTeX, 2 figures. Returning to v5 after erroneous
replacement. Apologie
Theory of Abelian Projection
Analytic methods for Abelian projection are developed. A number of results
are obtained related to string tension measurements. It is proven that even
without gauge fixing, abelian projection yields string tensions of the
underlying non-Abelian theory. Strong arguments are given for similar results
in the case where gauge fixing is employed. The methods used emphasize that the
projected theory is derived from the underlying non-Abelian theory rather than
vice versa. In general, the choice of subgroup used for projection is not very
important, and need not be Abelian. While gauge fixing is shown to be in
principle unnecessary for the success of Abelian projection, it is
computationally advantageous for the same reasons that improved operators,
e.g., the use of fat links, are advantageous in Wilson loop measurements. Two
other issues, Casimir scaling and the conflict between projection and critical
universality, are also discussed.Comment: Minor corrections, new section added, 14 pages, 3 figures, RevTe
Deconfinement Through Chiral Transition In 2 Flavour QCD
We propose that in QCD with dynamical quarks, colour deconfinement occurs
when an external field induced by the chiral condensate strongly aligns the
Polyakov loop. This effect sets in at the chiral symmetry restoration
temperature and thus makes deconfinement and chiral symmetry
restoration coincide. The predicted singular behavior of Polyakov loop
susceptibilities at is shown to be supported by finite temperature
lattice calculations.Comment: Talk given at Lattice 2000 (Finite Temperature), 4 pages, 6
EPS-figure
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
Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the -method
We determine the critical point and the ratios and
of critical exponents of the deconfinement transition in gauge theory
by applying the -method to Monte Carlo data of the modulus and the
square of the Polyakov loop. With the same technique we find from the Binder
cumulant its universal value at the critical point in the thermodynamical
limit to and for the next-to-leading exponent .
From the derivatives of the Polyakov loop dependent quantities we estimate then
. The result from the derivative of is , in
complete agreement with that of the Ising model.Comment: 11 pages, 3 Postscript figures, uses Plain Te
Extracting from small lattices: unquenched results
We calculate the response of the microscopic Dirac spectrum to an imaginary
isospin chemical potential for QCD with two dynamical flavors in the chiral
limit. This extends our previous calculation from the quenched to the
unquenched theory. The resulting spectral correlation function in the
-regime provides here, too, a new and efficient way to measure
on the lattice. We test the method in a hybrid Monte Carlo simulation
of the theory with two staggered quarks.Comment: 7 pages, 5 figure
- …