Cluster Monte Carlo and dynamical scaling for long-range interactions

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.