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SIGMA 3 (2007), 006, 14 pages hep-lat/0610043
https://doi.org/10.3842/SIGMA.2007.006
Contribution to the Proceedings of the O'Raifeartaigh Symposium
Generalized Potts-Models and their Relevance for Gauge Theories
Andreas Wipf a, Thomas Heinzl b, Tobias Kaestner a and Christian Wozar a
a) Theoretisch-Physikalisches Institut, Friedrich-Schiller-University Jena, Germany
b) School of Mathematics and Statistics, University of Plymouth, United Kingdom
Received October 05, 2006, in final form December 12, 2006; Published online January 05, 2007
Abstract
We study the Polyakov loop dynamics originating from
finite-temperature Yang-Mills theory. The effective actions
contain center-symmetric terms involving powers of the Polyakov
loop, each with its own coupling. For a subclass with two
couplings we perform a detailed analysis of the statistical
mechanics involved. To this end we employ a modified mean
field approximation and Monte Carlo simulations based on a novel
cluster algorithm. We find excellent agreement of both
approaches. The phase diagram exhibits both first and second
order transitions between symmetric, ferromagnetic and
antiferromagnetic phases with phase boundaries merging at three
tricritical points. The critical exponents ν and γ at
the continuous transition between symmetric and antiferromagnetic
phases are the same as for the 3-state spin Potts model.
Key words:
gauge theories; Potts models; Polyakov loop dynamics; mean field approximation; Monte Carlo simulations.
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