Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Some necessary background
- 3 Simple sampling Monte Carlo methods
- 4 Importance sampling Monte Carlo methods
- 5 More on importance sampling Monte Carlo methods for lattice systems
- 6 Off-lattice models
- 7 Reweighting methods
- 8 Quantum Monte Carlo methods
- 9 Monte Carlo renormalization group methods
- 10 Non-equilibrium and irreversible processes
- 11 Lattice gauge models: a brief introduction
- 12 A brief review of other methods of computer simulation
- 13 Monte Carlo methods outside of physics
- 14 Outlook
- Appendix: listing of programs mentioned in the text
- Index
12 - A brief review of other methods of computer simulation
Published online by Cambridge University Press: 21 November 2009
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Some necessary background
- 3 Simple sampling Monte Carlo methods
- 4 Importance sampling Monte Carlo methods
- 5 More on importance sampling Monte Carlo methods for lattice systems
- 6 Off-lattice models
- 7 Reweighting methods
- 8 Quantum Monte Carlo methods
- 9 Monte Carlo renormalization group methods
- 10 Non-equilibrium and irreversible processes
- 11 Lattice gauge models: a brief introduction
- 12 A brief review of other methods of computer simulation
- 13 Monte Carlo methods outside of physics
- 14 Outlook
- Appendix: listing of programs mentioned in the text
- Index
Summary
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
Integration methods (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 This is known as the NVE ensemble.
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- Information
- A Guide to Monte Carlo Simulations in Statistical Physics , pp. 363 - 382Publisher: Cambridge University PressPrint publication year: 2005