Non-Local effective SU(2) Polyakov-loop models from inverse Monte-Carlo methods

TL;DR

This paper investigates how well non-local Polyakov-loop models can describe SU(2) gluodynamics at finite temperature using inverse Monte-Carlo methods, focusing on the range and strength of non-local interactions.

Contribution

It systematically tests and characterizes non-local Polyakov-loop models for SU(2) gauge theory, including higher representations and interaction ranges, using inverse Monte-Carlo techniques.

Findings

Non-local couplings decay with distance, influenced by gauge coupling.

Higher representations and larger volumes extend the interaction range.

Results align with existing proposals for non-local effective actions.

Abstract

The strong-coupling expansion of the lattice gauge action leads to Polyakov-loop models that effectively describe gluodynamics at low temperatures, and together with the hopping expansion of the fermion determinant provides insight into the QCD phase diagram at finite density and low temperatures, although for rather heavy quarks. At higher temperatures the strong-coupling expansion breaks down and it is expected that the interactions between Polyakov loops become non-local. Here, we therefore test how well pure SU(2) gluodynamics can be mapped onto different non-local Polyakov models with inverse Monte-Carlo methods. We take into account Polyakov loops in higher representations and gradually add interaction terms at larger distances. We are particularly interested in extrapolating the range of non-local terms in sufficiently large volumes and higher representations. We study the characteristic fall-off in strength of the non-local couplings with the interaction distance, and its dependence on the gauge coupling in order to compare our results to existing proposals for non-local effective actions.