Eur. Phys. J. Special Topics 226, 581-594 (2017)
https://doi.org/10.1140/epjst/e2016-60338-3

Regular Article

Cluster Monte Carlo and dynamical scaling for long-range interactions

¹ Applied Mathematics Research Centre, Coventry University, Coventry CV1 5FB, United Kingdom
² Institut Jean Lamour, CNRS/UMR 7198, Groupe de Physique Statistique, Université de Lorraine, BP 70239, F-54506 Vandœuvre-les-Nancy Cedex, France
³ Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L⁴), 04009 Leipzig, Germany

^a e-mail: martin.weigel@coventry.ac.uk

Received: 21 October 2016
Revised: 17 November 2016
Published online: 5 April 2017

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(N²) 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.