Cluster Monte Carlo and dynamical scaling for long-range interactions

TL;DR

This paper reviews and introduces efficient cluster algorithms for simulating long-range interacting spin systems, demonstrating improved computational scaling and analyzing their dynamical properties in the Ising model.

Contribution

The paper proposes a new single-cluster algorithm variant that enhances simulation efficiency for long-range interactions in spin systems.

Findings

Algorithms reduce computational effort from O(N^2) to O(N log N) or O(N)

The new algorithm shows improved dynamical scaling in the Ising model

Efficiency gains are demonstrated for power-law decaying interactions

Abstract

Many spin systems affected by critical slowing down can be efficiently simulated using cluster algorithms. Where such systems have long-range interactions, suitable formulations can additionally bring down the computational effort for each update from O($N^2$) to O($N\ln N$) or even O($N$), thus promising an even more dramatic computational speed-up. Here, we review the available algorithms and propose a new and particularly efficient single-cluster variant. The efficiency and dynamical scaling of the available algorithms are investigated for the Ising model with power-law decaying interactions.