SIMULATION OF ORDER TRANSITIONS ON A PARALLEL COMPUTER

The traditional Monte Carlo simulation of order transitions in a ferro magnet (or in a binary crystalline alloy) is carried out by generating a sequence of local swaps (spin reversals or exchanges of atoms) on a finite lattice, each of which in turn is accepted or rejected accordi ng to probabilities prescribed by Metropolis et al., and thus creating a sample from the limit distribution of the resulting Markov chain. T he limit can, however, take a long time to reach, especially near crit ical temperatures, if the lattice used is large enough to mask boundar y effects. Since the probability is fairly small that successive swaps in the sequence involve directly interacting lattice sites, it makes sense to save time by performing them simultaneously where possible, b y running the simulation on a parallel computer. This report discusses , at an elementary level, some of the theoretical and practical questi ons that can arise in doing so. (C) 1998 IMACS/Elsevier Science B.V.