Chapter 14 - Accelerating Monte Carlo Sampling

Abstract

This chapter discusses various advanced Monte Carlo (MC) techniques. The method of parallel tempering provides good sampling of systems that have a free energy landscape with many local minima. It resembles the technique of simulating annealing and is related to several other schemes such as the extended-ensemble method, simulated tempering, and J-walking. The idea of parallel tempering is to include MC trial moves that attempt to “swap” systems that belong to different thermodynamic states. The basic idea behind the hybrid MC scheme is that one can use Molecular Dynamics (MD) to generate MC trial moves. For every trial move, the particle velocities are chosen at random from a Maxwell distribution. It is often advantageous to construct a trial move that consists of a sequence of MD steps. Yet, one cannot make the time step for a single hybrid MC move too long because then the acceptance would become very small. It is also interesting to use hybrid MC on models that have an expensive (many-body) potential energy function that may, to a first approximation, be modeled using a cheap (pair) potential. One of the differences of simulations of models with continuous interactions compared to those of models with hard-core potentials is the way in which MC moves are optimized.