Cluster Percolation and Explicit Symmetry Breaking in Spin Models

TL;DR

This paper explores how spin clusters in models like Potts and O(n) relate to phase transitions, especially under external fields that explicitly break symmetry, revealing persistent connections with thermal properties.

Contribution

It introduces an analysis of spin cluster behavior under explicit symmetry breaking, extending the geometric interpretation of phase transitions in spin models.

Findings

Clusters maintain relationships with thermal features despite symmetry breaking

External fields modify but do not eliminate the percolation transition

Geometric and thermal properties remain interconnected under explicit symmetry breaking

Abstract

Many features of spin models can be interpreted in geometrical terms by means of the properties of well defined clusters of spins. In case of spontaneous symmetry breaking, the phase transition of models like the q-state Potts model, O(n), etc., can be equivalently described as a percolation transition of clusters. We study here the behaviour of such clusters when the presence of an external field H breaks explicitly the global symmetry of the Hamiltonian of the theory. We find that these clusters have still some interesting relationships with thermal features of the model.