Generalized Potts-Models and their Relevance for Gauge Theories

Details Generalized Potts-Models and their Relevance for Gauge Theories Generalized Potts-Models and their Relevance for Gauge Theories

2006-10-06

arxiv.org/abs/hep-lat/0610043v2

SIGMA 3:006,2007

Physics

High Energy Physics

High Energy Physics - Lattice

This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (

Scientific paper

10.3842/SIGMA.2007.006

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 $\nu$ and $\gamma$ at the continuous transition between symmetric and antiferromagnetic phases are the same as for the 3-state spin Potts model.

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