Equilibrium criterion and effective spin models for finite temperature gauge theories

TL;DR

This paper develops an effective 3D model for finite temperature SU(2) gauge theories using Polyakov loops, applying an equilibrium criterion to identify essential operators that accurately reproduce key observables.

Contribution

It introduces a systematic method to determine the minimal effective action for gauge theories based on an equilibrium self-consistency condition.

Findings

The effective model reproduces Polyakov loop averages accurately.

Application of the criterion reduces the number of operators needed.

The approach is demonstrated on SU(2) gauge theory in 3+1 dimensions.

Abstract

Using the example of the SU(2) gauge theory in 3+1 dimensions we consider the construction of a 3-dimensional effective model in terms of Polyakov loops. We demonstrate the application of an equilibrium self-consistency condition to the systematic analysis of the contribution of various (global Z(2) symmetric) terms in the effective model action. We apply this analysis to the construction of a simple effective action with the minimum necessary number of operators. Such an action is shown to be capable of reproducing relevant observables, e.g. the Polyakov loop ensemble average, within the desired accuracy.