Accelerating markov chain monte carlo simulation through sequential updating and parallel computing

Monte Carlo simulation is a statistical sampling method used in studies of physical systems with properties that cannot be easily obtained analytically. The phase behavior of the Restricted Primitive Model of electrolyte solutions on the simple cubic lattice is studied using grand canonical Monte Carlo simulations and finite-size scaling techniques. The transition between disordered and ordered, NaCl-like structures is continuous, second-order at high temperatures and discrete, first-order at low temperatures. The line of continuous transitions meets the line of first-order transitions at a tricritical point. A new algorithm-Random Skipping Sequential (RSS) Monte Carl—is proposed, justified and shown analytically to have better mobility over the phase space than the conventional Metropolis algorithm satisfying strict detailed balance. The new algorithm employs sequential updating, and yields greatly enhanced sampling statistics than the Metropolis algorithm with random updating. A parallel version of Markov chain theory is introduced and applied in accelerating Monte Carlo simulation via cluster computing. It is shown that sequential updating is the key to reduce the inter-processor communication or synchronization which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time by the new method for systems of large and moderate sizes.