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.
Flores-Sola, E., Weigel, M., Kenna, R., & Berche, B. (2017). Cluster Monte Carlo and dynamical scaling for long-range interactions. The European Physical Journal Special Topics, 226(4), 581 - 594. https://doi.org/10.1140/epjst/e2016-60338-3