Cluster Percolation and Thermal Critical Behaviour

TL;DR

This paper explores the connection between percolation theory and phase transitions in spin systems and gauge theories, proposing a geometric perspective on deconfinement and critical phenomena, especially under external fields.

Contribution

It reviews the equivalence of phase transitions and percolation in spin systems and extends this concept to SU(2) gauge theory, introducing an H-dependent cluster definition relevant for QCD.

Findings

Percolation describes continuous phase transitions in spin systems.

The percolation perspective applies to the deconfinement transition in SU(2) gauge theory.

An H-dependent cluster definition is necessary for describing transitions under external fields.

Abstract

Continuous phase transitions in spin systems can be formulated as percolation of suitably defined clusters. We review this equivalence and then discuss how in a similar way, the color deconfinement transition in SU(2) gauge theory can be treated as a percolation phenomenon. In the presence of an external field, spin systems cease to show thermal critical behavior, but the geometric percolation transition persists (Kert\'esz line). For $H\not=0$, we study the relation between percolation and pseudocritical behavior, both for continuous and first order transitions, and show that it leads to the necessity of an $H$-dependent cluster definition. A viable formulation of this kind could serve as definition of deconfinement in QCD with dynamical quarks.