Synchronous Relaxation for Parallel Ising Spin Simulations

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A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm citeBKL75, which is efficient but is 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'' citeCS8 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 processed 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.