Invaded cluster algorithm for equilibrium critical points

TL;DR

The paper introduces an invasion percolation-based cluster algorithm that efficiently finds critical points in spin systems without prior temperature knowledge, demonstrated on Ising models.

Contribution

It presents a novel invasion cluster algorithm that quickly equilibrates spin configurations and accurately determines critical temperatures without prior system information.

Findings

Faster equilibration than Swendsen-Wang algorithm

Accurately locates critical points in 2D and 3D Ising models

Provides a new tool for studying critical phenomena

Abstract

A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical temperature and other observables in the critical region. The method is illustrated for the two- and three-dimensional Ising models. The algorithm equilibrates spin configurations much faster than the closely related Swendsen-Wang algorithm.