Spatial updating grand canonical Monte Carlo algorithms for fluid simulation: generalization to continuous potentials and parallel implementation.

Spatial updating grand canonical Monte Carlo algorithms are generalizations of random and sequential updating algorithms for lattice systems to continuum fluid models. The elementary steps, insertions or removals, are constructed by generating points in space either at random (random updating) or in a prescribed order (sequential updating). These algorithms have previously been developed only for systems of impenetrable spheres for which no particle overlap occurs. In this work, spatial updating grand canonical algorithms are generalized to continuous, soft-core potentials to account for overlapping configurations. Results on two- and three-dimensional Lennard-Jones fluids indicate that spatial updating grand canonical algorithms, both random and sequential, converge faster than standard grand canonical algorithms. Spatial algorithms based on sequential updating not only exhibit the fastest convergence but also are ideal for parallel implementation due to the absence of strict detailed balance and the nature of the updating that minimizes interprocessor communication. Parallel simulation results for three-dimensional Lennard-Jones fluids show a substantial reduction of simulation time for systems of moderate and large size. The efficiency improvement by parallel processing through domain decomposition is always in addition to the efficiency improvement by sequential updating.

Parallel Markov chain Monte Carlo simulations.

With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor 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 for systems of moderate and large size.

Simulation of symmetric tricritical behavior in electrolytes.

Despite extensive experimental, theoretical, and simulation efforts, a unified description of ionic phase transitions and criticality has not yet emerged. In this work, we investigate the phase behavior of the restricted primitive model of electrolyte solutions on the simple cubic lattice using grand canonical Monte Carlo simulations and finite-size scaling techniques. The phase diagram of the system is distinctly different from its continuum-space analog. We find order-disorder transitions for reduced temperatures T* < or approximately 0.51, where the ordered structures resemble those of the NaCl crystal. The order-disorder transition is continuous for 0.15 < or approximately T* < or approximately 0.51 and becomes first order at lower temperatures. The line of first-order transitions is a line of three-phase coexistence between a disordered and two ordered phases. The line of continuous, second-order transitions meets this line of triple points at a tricritical point at T* approximately equal to 0.1475. We locate the line of continuous transitions, and the line of triple points using finite-size scaling techniques. The tricritical temperature is estimated by extrapolation of the size-dependent tricritical temperatures obtained from a sixth-order Landau expansion of the free energy. Our calculated phase diagram is in qualitative agreement with mean-field theories.

Scaling fields and pressure mixing in the Widom-Rowlinson model.

We address the issues of scaling fields and of pressure mixing in the penetrable sphere model. This model has an exact symmetry locus from which analytical results may be derived. Based on exact results, we demonstrate that the scaling fields are analytic functions of temperature and chemical potential only. We conclude that there is no pressure mixing in this model. Our findings are in accord with numerical simulations for the same model.

Acceleration of Markov chain Monte Carlo simulations through sequential updating.

Strict detailed balance is not necessary for Markov chain Monte Carlo simulations to converge to the correct equilibrium distribution. In this work, we propose a new algorithm which only satisfies the weaker balance condition, and it is shown analytically to have better mobility over the phase space than the Metropolis algorithm satisfying strict detailed balance. The new algorithm employs sequential updating and yields better sampling statistics than the Metropolis algorithm with random updating. We illustrate the efficiency of the new algorithm on the two-dimensional Ising model. The algorithm is shown to identify the correct equilibrium distribution and to converge faster than the Metropolis algorithm with strict detailed balance. The main advantages of the new algorithm are its simplicity and the feasibility of parallel implementation through domain decomposition.