Cluster Algorithms for Spin Models on MIMD Parallel Computers

Parallel computers are ideally suited to the Monte Carlo simulation of spin models using the standard Metropolis algorithm, since it is regular and local. However local algorithms have the major drawback that near a phase transition the number of sweeps needed to generate a statistically independent configuration increases as the square of the lattice size. New algorithms have recently been developed which dramatically reduce this ‘critical slowing down’ by updating clusters of spins at a time. The highly irregular and non-local nature of these algorithms means that they are much more difficult to parallelize efficiently. Here we introduce the new cluster algorithms, explain some sequential algorithms for identifying and labelling connected clusters of spins, and then outline some parallel algorithms which have been implemented on MIMD machines.