INTRODUCTION

In the previous chapters of this text we have examined a wide variety of Monte Carlo methods in depth. Although these are exceedingly useful for many different problems in statistical physics, there are some circumstances in which the systems of interest are not well suited to Monte Carlo study. Indeed there are some problems which may not be treatable by stochastic methods at all, since the time-dependent properties as constrained by deterministic equations of motion are the subject of the study. The purpose of this chapter is thus to provide a very brief overview of some of the other important simulation techniques in statistical physics. Our goal is not to present a complete list of other methods or even a thorough discussion of these methods which are included but rather to offer sufficient background to enable the reader to compare some of the different approaches and better understand the strengths and limitations of Monte Carlo simulations.

MOLECULAR DYNAMICS

Integrationmethods (microcanonical ensemble)

Molecular dynamics methods are those techniques which are used to numerically integrate coupled equations of motion for a system which may be derived, e.g. in the simplest case from Lagrange's equations or Hamilton's equations. Thus, the approach chosen is to deal with many interacting atoms or molecules within the framework of classical mechanics. We begin this discussion with consideration of systems in which the number of particles N, the system volume V, and the total energy of the system E are held constant.