Multibondic Cluster Algorithm for Monte Carlo Simulations of First-Order Phase Transitions

TL;DR

This paper introduces a novel multibondic cluster algorithm for Monte Carlo simulations of first-order phase transitions in q-state Potts models, combining cluster updates with reweighting techniques to improve efficiency.

Contribution

It presents a new algorithm that integrates cluster updates with bond configuration reweighting, enhancing simulation performance for first-order phase transitions.

Findings

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

Algorithm performs effectively for q=7, 10, 20 models.

Numerical tests validate the efficiency of the proposed method.

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 $\alpha \approx 1$.