Effective Polyakov-loop theory for pure Yang-Mills from strong coupling expansion

TL;DR

This paper derives effective 3D spin models for finite-temperature lattice Yang-Mills theories using strong-coupling expansions, enabling accurate numerical predictions of deconfinement transitions.

Contribution

It introduces a formulation for effective Polyakov-loop actions in SU(2) and SU(3) that allows for Monte Carlo analysis and precise predictions of deconfinement points.

Findings

Accurately predicts deconfinement points within a few percent

Develops effective actions incorporating higher order corrections

Enables numerical investigation of phase transitions in pure gauge theories

Abstract

Lattice Yang-Mills theories at finite temperature can be mapped onto effective 3d spin systems, thus facilitating their numerical investigation. Using strong-coupling expansions we derive effective actions for Polyakov loops in the $SU(2)$ and $SU(3)$ cases and investigate the effect of higher order corrections. Once a formulation is obtained which allows for Monte Carlo analysis, the nature of the phase transition in both classes of models is investigated numerically, and the results are then used to predict -- with an accuracy within a few percent -- the deconfinement point in the original 4d Yang-Mills pure gauge theories, for a series of values of $N_\tau$ at once.