Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 006, 14 pages      hep-lat/0610043
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

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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