Multicanonical Cluster Algorithm and the 2-D 7-State Potts Model

TL;DR

This paper introduces a hybrid multicanonical cluster algorithm that effectively overcomes supercritical slowing down in simulating the 2D 7-state Potts model, enabling efficient exploration of metastable states in large systems.

Contribution

A novel hybrid algorithm combining microcanonical demons with multicanonical updates, improving simulation efficiency for first-order phase transitions.

Findings

Tunnelling time scales as L^{1.82} for system size L.

Algorithm successfully applied to systems up to 128^2 volume.

Effectively eliminates supercritical slowing down in first-order transitions.

Abstract

I present a hybrid-like two-step algorithm, which combines a microcanonical update of a spin system using demons, with a multicanonical demon refresh. The algorithm is free from the supercritical slowing down that burdens the canonical methods: the exponential increase of the tunnelling time between the metastable states in the first-order phase transitions, when the volume of the system is increased. The demons act as a buffer between the multicanonical heat bath and the spin system, allowing the spin system to be updated with any microcanonical demon procedure, including cluster methods. The cluster algorithm is demonstrated with the 2-dimensional 7-state Potts model, using volumes up to $128^2$. The tunnelling time is found to increase as $L^{1.82}$, where $L$ is the linear dimension of the system.