Efficient Monte Carlo Simulation Methods in Statistical Physics

Abstract

The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in statistical physics. We discuss their advantages, applications, and some challenge problems which are still awaiting for better solutions. We discuss some of the recent development in simulation where reweighting is used, such as histogram methods and multicanonical method. We then discuss the transition matrix Monte Carlo method and associated algorithms. The transition matrix method offers an efficient way to compute the density of states. Thus entropy and free energy, as well as the usual thermodynamic averages, are obtained as functions of model parameter (e.g. temperature) in a single run. New sampling algorithms, such as the flat histogram algorithm and equal-hit algorithm, offer sampling techniques which generate uniform probability distribution for some chosen macroscopic variable.