Generalized Potts-Models and their Relevance for Gauge Theories

TL;DR

This paper investigates the phase structure of Polyakov loop models derived from finite-temperature Yang-Mills theory, using analytical and numerical methods to reveal complex phase transitions and critical behavior.

Contribution

It introduces a detailed analysis of a subclass of Polyakov loop models with two couplings, employing a modified mean field approach and a novel cluster Monte Carlo algorithm.

Findings

Excellent agreement between mean field and Monte Carlo results

Phase diagram includes first and second order transitions with tricritical points

Critical exponents match those of the 3-state spin Potts model

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