Synchronous Relaxation for Parallel Ising Spin Simulations

A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm [BKL75], which is efficient but turns out to be hard to parallelize using conservative methods. Our parallel algorithm is optimistic. Unlike other optimistic algorithms, e.g., Time Warp, our algorithm is synchronous. It also belongs to the class of simulations known as "relaxation" [CS89]; hence it is named "synchronous relaxation." We derive performance guarantees for this algorithm. If N is the number of PEs, then under weak assumptions we show that the number of correct events procesed per unit of time is, on average, at least of order N/ log N. All communication delays, processing time, and busy waits are taken into account.