Multibondic Cluster Algorithm

TL;DR

This paper introduces a novel multibondic cluster algorithm for q-state Potts models that combines cluster updates with reweighting, achieving near-optimal autocorrelation scaling for simulating first-order phase transitions.

Contribution

It proposes a new algorithm integrating cluster updates with reweighting in the Fortuin-Kasteleyn representation, improving simulation efficiency for first-order phase transitions.

Findings

Autocorrelation times grow as V^1, indicating optimal random walk behavior.

Numerical tests for q=7, 10, 20 demonstrate the algorithm's effectiveness.

The method enhances simulation performance for first-order phase transitions.

Abstract

Inspired by the multicanonical approach to simulations of first-order phase transitions we propose for $q$-state Potts models a combination of cluster updates with reweighting of the bond configurations in the Fortuin-Kastelein-Swendsen-Wang representation of this model. Numerical tests for the two-dimensional models with $q=7, 10$ and $20$ show that the autocorrelation times of this algorithm grow with the system size $V$ as $\tau \propto V^\alpha$, where the exponent takes the optimal random walk value of $\alpha \approx 1$.