Site Percolation and Phase Transitions in Two Dimensions

TL;DR

This paper investigates the percolation properties of pure-site clusters in two-dimensional spin models, demonstrating that percolation transitions coincide with thermal critical points across various models, including gauge theories.

Contribution

It extends the understanding of percolation in 2D systems by showing the universality of percolation transitions at the critical point for a broad class of models.

Findings

Percolation transition occurs at the same point as the thermal transition.

Critical exponents differ from thermal ones but are universal within the same class.

Numerical evidence supports the universality across different models.

Abstract

The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters undergo a percolation transition exactly at the critical point. We show that this result is valid for a wide class of bidimensional systems undergoing a continuous magnetization transition. We provide numerical evidence for discrete as well as for continuous spin models, including SU(N) lattice gauge theories. The critical percolation exponents do not coincide with the ones of the thermal transition, but they are the same for models belonging to the same universality class.