Percolation and Critical Behaviour in SU(2) Gauge Theory

TL;DR

This paper investigates the confinement-deconfinement transition in SU(2) gauge theory using a percolation framework inspired by the Ising model, demonstrating a successful geometric description across different lattice regularizations.

Contribution

It extends the percolation description of phase transitions from the Ising model to SU(2) gauge theory, introducing a cluster definition based on effective Ising-like theories.

Findings

Percolation transition describes the confinement-deconfinement phase change.

The geometric transition aligns with the thermal transition in SU(2).

Results are consistent across two lattice regularizations.

Abstract

The paramagnetic-ferromagnetic transition in the Ising model can be described as percolation of suitably defined clusters. We have tried to extend such picture to the confinement-deconfinement transition of SU(2) pure gauge theory, which is in the same universality class of the Ising model. The cluster definition is derived by approximating SU(2) by means of Ising-like effective theories. The geometrical transition of such clusters turns out to describe successfully the thermal counterpart for two different lattice regularizations of (3+1)-d SU(2).