Graphical representations and cluster algorithms for critical points with fields

TL;DR

This paper introduces a graphical representation and cluster algorithm for ferromagnetic Ising models with arbitrary fields, linking critical points to percolation thresholds and demonstrating efficient simulation performance.

Contribution

A novel two-replica graphical representation and cluster algorithm applicable to Ising systems with arbitrary fields, connecting critical points to percolation phenomena.

Findings

Critical points correspond to percolation thresholds.

The algorithm has a dynamic exponent less than 0.5.

Numerical simulations validate the approach.

Abstract

A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are associated with the percolation threshold of the graphical representation. Results from numerical simulations of the Ising model in a staggered field are presented. The dynamic exponent for the algorithm is measured to be less than 0.5.