Cluster Percolation and Pseudocritical Behaviour in Spin Models

TL;DR

This paper explores how percolation theory applies to spin models under external magnetic fields, revealing that percolation transitions align with pseudocritical points in the 2D Ising and 3D O(2) models through Monte Carlo simulations.

Contribution

It demonstrates the equivalence of percolation critical lines and pseudocritical points in spin models with external fields, extending understanding of phase transition phenomena.

Findings

Percolation critical lines match pseudocritical points in small fields.

Percolation clusters remain well-defined under external magnetic fields.

Monte Carlo simulations confirm the theoretical relationship.

Abstract

The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition, even though the system no longer shows thermal critical behaviour. We investigate the 2-dimensional Ising model and the 3-dimensional O(2) model by means of Monte Carlo simulations. We find for small fields that the line of percolation critical points has the same functional form as the line of thermal pseudocritical points.