Cluster Identification Algorithms for Spin Models — Sequential and Parallel

Abstract

Monte Carlo cluster update algorithms are extremely efficient for simulating spin models near their phase transitions, where local update algorithms suffer severe critical slowing down. Unfortunately, as the cluster algorithms are highly irregular as well as nonlocal, they are much more difficult to parallelize efficiently. The main difficulty lies in identifying which spins belong to which cluster. In this paper we investigate a number of cluster identification algorithms, both sequential and parallel, which we have implemented on serial, SIMD and MIMD computers.