Spatial updating Monte Carlo algorithms in particle simulations

Abstract

Spatial updating is a generalisation of random and sequential updating algorithms for Ising and lattice-gas systems to off-lattice, continuum fluid models. By analogy with a lattice-gas, spatial updating is implemented in the grand canonical ensemble by selecting a point in space and deducing the type of move by examining the local environment around the point. In this work, spatial updating is combined with simulated tempering techniques to determine the phase behaviour of a square-well fluid with an interaction range 1.15σ, where σ is the particle diameter. In the remaining part of this work, spatial updating is extended to very high densities by allowing volume fluctuations. In the resulting ensemble, a prototype of great grand canonical ensemble, fluctuations are unbounded and a constraint or a restriction must be imposed. Each simulation of the constrained great grand canonical ensemble requires a set of weights that are determined iteratively. The main outcome of a single simulation in the constrained great grand canonical ensemble is the density of states in terms of all its independent extensive variables, which allows for the determination of absolute free energies and entropies. Results obtained on a system of hard spheres demonstrate the validity of this technique.

Keywords:

• Monte Carlo
• phase transitions
• finite-size scaling

Acknowledgements

Financial support from NSF, CBET-0652131 and CBET-0967291 is gratefully acknowledged.