Simulation of phase transitions via spatial updating and tempering

Abstract

In spatial updating grand canonical Monte Carlo, the elementary moves are implemented either by selecting points in space at random (random updating) or in a predetermined order (sequential updating). Previous work indicates that spatial updating is more efficient than standard updating and is ideal for parallel processing via domain decomposition. In this work, it is shown that the combination of spatial updating grand canonical Monte Carlo with tempering techniques can increase the simulation efficiency of phase transitions by several orders of magnitude. In simulated tempering, several macrostates are coupled together to form a super-ensemble or an expanded ensemble. Each macrostate comprises a grand canonical system at a given value of the chemical potential and the temperature. The elementary steps consist of particle transfers as well as switches between different macrostates. The switches can be implemented according to a Metropolis or a heat-bath algorithm. The combination of spatial updating with tempering is used in the investigation of the vapour–liquid transition of the 2D Lennard-Jones fluid. The critical parameters are estimated from finite-size scaling techniques using a Landau expansion of the free energy density. In the near-critical region, the efficiency enhancement is two to four orders of magnitude higher than conventional algorithms. The increased efficiency and the feasibility of parallel processing allows for simulations of much larger systems than is possible with standard algorithms.