(360g) Sequential Updating Algorithms for Grand Canonical Monte Carlo Simulations

Strict detailed balance is essentially unnecessary for Markov chain Monte Carlo simulations to converge to the correct equilibrium distribution. Recently, we proposed [1] a general Monte Carlo algorithm that only satisfies the weaker balance condition. The new algorithm is based on sequential updating with partial randomness to guarantee correct sampling. We have shown analytically that the new algorithm identifies the correct equilibrium distribution of states. Analysis of the diagonal elements of the transition matrices shows that the new algorithm is more ?mobile? than the conventional Metropolis algorithm. Eigenvalue analysis for small systems indicates that the new algorithm converges faster than the Metropolis algorithm with strict detailed balance. Monte Carlo simulations of the Ising model and the lattice gas show that the new algorithm reduces autocorrelation time and thus improves the statistical quality of sampling. By exploiting the equivalence of the Ising model and the lattice gas, we demonstrate that the new method can be readily applied to continuum systems, such as Lennard-Jones, in the grand canonical ensemble. Potential applications of the new algorithm are simulations of 1st and 2nd order phase transitions. Parallel Monte Carlo simulations based on spatial decomposition suffer from loss of precision due to the periodic switching of active domains. On the other hand, the new algorithm, which is intrinsically sequential, can be parallelized easily without compromising precision.

[1] Ruichao Ren and G. Orkoulas, J. Chem. Phys. 124, 064109 (2006)