Book contents
- A Guide to Monte Carlo Simulations in Statistical Physics
- A Guide to Monte Carlo Simulations in Statistical Physics
- Copyright page
- 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 simulations at the periphery of physics and beyond
- 14 Monte Carlo studies of biological molecules
- 15 Emerging trends
- Index
- References
6 - Off-lattice models
Published online by Cambridge University Press: 24 November 2021
- A Guide to Monte Carlo Simulations in Statistical Physics
- A Guide to Monte Carlo Simulations in Statistical Physics
- Copyright page
- 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 simulations at the periphery of physics and beyond
- 14 Monte Carlo studies of biological molecules
- 15 Emerging trends
- Index
- References
Summary
The examination of the equation of state of a two-dimensional model fluid (the hard disk system) was the very first application of the importance sampling Monte Carlo method in statistical mechanics (Metropolis et al., 1953), and since then the study of both atomic and molecular fluids by Monte Carlo simulation has been a very active area of research. Remember that statistical mechanics can deal well analytically with very dilute fluids (ideal gases), and it can also deal well with crystalline solids (making use of the harmonic approximation and perfect crystal lattice periodicity and symmetry), but the treatment of strongly correlated dense fluids (and their solid counterparts, amorphous glasses) is much more difficult. Even the description of short range order in fluids in a thermodynamic state far away from any phase transition is a non-trivial matter (unlike the lattice models discussed in Chapter 5, where far away from phase transitions the molecular field approximation, or a variant thereof, is usually both good enough and easily worked out, and the real interest is generally in phase transition problems).
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- Information
- A Guide to Monte Carlo Simulations in Statistical Physics , pp. 243 - 325Publisher: Cambridge University PressPrint publication year: 2021