Effective Actions for the SU(2) Confinement-Deconfinement Phase Transition

TL;DR

This paper compares various effective Polyakov loop actions for SU(2) Yang-Mills theory at finite temperature, using inverse Monte Carlo and mean-field methods to identify models that accurately reproduce key observables.

Contribution

It introduces a novel mean-field approach and applies inverse Monte Carlo techniques to determine effective couplings, improving understanding of the confinement-deconfinement transition.

Findings

Mean-field analysis closely matches Monte Carlo results.

Effective actions reproduce standard Yang-Mills observables well.

Nearest-neighbor models capture essential physics with some limitations.

Abstract

We compare different Polyakov loop actions yielding effective descriptions of finite-temperature SU(2) Yang-Mills theory on the lattice. The actions are motivated by a simultaneous strong-coupling and character expansion obeying center symmetry and include both Ising and Ginzburg-Landau type models. To keep things simple we limit ourselves to nearest-neighbor interactions. Some truncations involving the most relevant characters are studied within a novel mean-field approximation. Using inverse Monte-Carlo techniques based on exact geometrical Schwinger-Dyson equations we determine the effective couplings of the Polyakov loop actions. Monte-Carlo simulations of these actions reveal that the mean-field analysis is a fairly good guide to the physics involved. Our Polyakov loop actions reproduce standard Yang-Mills observables well up to limitations due to the nearest-neighbor approximation.