Percolation and Deconfinement in SU(2) Gauge Theory

TL;DR

This paper demonstrates that the deconfinement transition in SU(2) gauge theory can be understood as a percolation transition of Polyakov loop clusters, aligning with the universality class of the Ising model.

Contribution

It introduces a percolation-based description of deconfinement in SU(2) gauge theory using Fortuin-Kasteleyn bonds, matching the critical exponents of the traditional order parameter.

Findings

Deconfinement transition corresponds to percolation of Polyakov loop clusters.

Percolation description yields the same critical exponents as the order-disorder transition.

SU(2) gauge theory and Ising model share the same universality class.

Abstract

The deconfinement transition in SU(2) gauge theory and the magnetization transition in the Ising model belong to the same universality class. The critical behaviour of the Ising model can be characterized either as spontaneous breaking of the $Z_2$ symmetry of spin states or as percolation of appropriately defined spin clusters. We show that deconfinement in SU(2) gauge theory can be specified as percolation of Polyakov loop clusters with Fortuin-Kasteleyn bond weights, leading to the same critical exponents as the conventional order-disorder description based on the Polykov loop expectation value.