Cluster Percolation and Chiral Phase Transition

TL;DR

This paper investigates the geometric properties of clusters in fermion lattice models using the Meron Cluster algorithm, revealing a percolation transition at the chiral critical temperature similar to spin model percolation.

Contribution

It introduces a novel percolation perspective on the chiral phase transition in fermion models via cluster geometry analysis.

Findings

Identification of a generalized percolation transition at the chiral critical temperature

Cluster geometrical features suggest a percolation phase transition analogous to spin models

Application of the Meron Cluster algorithm to study geometrical aspects of fermion models

Abstract

The Meron Cluster algorithm solves the sign problem in a class of interacting fermion lattice models with a chiral phase transition. Within this framework, we study the geometrical features of the clusters built by the algorithm, that suggest the occurrence of a generalized percolating phase transition at the chiral critical temperature in close analogy with Fortuin-Kasteleyn percolation in spin models.