Sequential updating algorithms for grand canonical Monte Carlo simulations

Abstract

Strict detailed balance is essentially unnecessary for Markov chain Monte Carlo simulations to converge to the correct equilibrium distribution. Recently, we proposed a Monte Carlo algorithm based on sequential updating moves with partial randomness to guarantee correct sampling. The proposed algorithm only satisfies the weaker balance condition and converges faster than the Metropolis algorithm with strict detailed balance. In this work, we illustrate the efficiency of the algorithm for the two-dimensional lattice gas model in the grand canonical ensemble. Parallel implementation of the sequential algorithm on lattice systems indicates that parallel Monte Carlo simulations, if treated correctly, are not only as precise as serial implementation, but can also save significant computing time.

Keywords:

• Monte Carlo
• Sequential updating
• Grand canonical
• Parallel simulation

Acknowledgements

The authors appreciate the encouragement and interest of Professor P. D. Christofides. The calculations were performed on Intel Xeon processors awarded to G.O. through Intel Higher Education Program Equipment Grants.