Z_3 Polyakov Loop Models and Inverse Monte-Carlo Methods

TL;DR

This paper investigates effective Z_3 Polyakov loop models for SU(3) Yang-Mills theory at finite temperature, combining mean field analysis, Monte-Carlo simulations, and inverse methods to understand phase structure and determine effective couplings.

Contribution

It provides a comprehensive analysis of phase diagrams and employs inverse Monte-Carlo methods to accurately match effective models to Yang-Mills theory.

Findings

Rich phase structure including ferromagnetic and antiferromagnetic phases

Mean field results agree well with Monte-Carlo data near tricritical points

Critical exponents match those of the Z_3 Potts model

Abstract

We study effective Polyakov loop models for SU(3) Yang-Mills theory at finite temperature. A comprehensive mean field analysis of the phase diagram is carried out and compared to the results obtained from Monte-Carlo simulations. We find a rich phase structure including ferromagnetic and antiferromagnetic phases. Due to the presence of a tricritical point the mean field approximation agrees very well with the numerical data. Critical exponents associated with second-order transitions coincide with those of the Z_3 Potts model. Finally, we employ inverse Monte-Carlo methods to determine the effective couplings in order to match the effective models to Yang-Mills theory.