A Guide to Monte Carlo Simulations in Statistical Physics,9780521842389

A Guide to Monte Carlo Simulations in Statistical Physics

by
Edition: 2nd
ISBN13: 9780521842389
ISBN10: 0521842387
Format: Hardcover
Pub. Date: 2005-09-19
Publisher(s): Cambridge University Press
List Price: $104.84

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Summary

This new and updated edition deals with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics, statistical mechanics, and related fields. After briefly recalling essential background in statistical mechanics and probability theory, it gives a succinct overview of simple sampling methods. The concepts behind the simulation algorithms are explained comprehensively, as are the techniques for efficient evaluation of system configurations generated by simulation. It contains many applications, examples, and exercises to help the reader and provides many new references to more specialized literature. This edition includes a brief overview of other methods of computer simulation and an outlook for the use of Monte Carlo simulations in disciplines beyond physics. This is an excellent guide for graduate students and researchers who use computer simulations in their research. It can be used as a textbook for graduate courses on computer simulations in physics and related disciplines.

Table of Contents

Preface xii
Introduction
1(6)
What is a Monte Carlo simulation?
1(1)
What problems can we solve with it?
2(1)
What difficulties will we encounter?
3(1)
Limited computer time and memory
3(1)
Statistical and other errors
3(1)
What strategy should we follow in approaching a problem?
4(1)
How do simulations relate to theory and experiment?
4(2)
Perspective
6(1)
Some necessary background
7(41)
Thermodynamics and statistical mechanics: a quick reminder
7(20)
Basic notions
7(6)
Phase transitions
13(11)
Ergodicity and broken symmetry
24(1)
Fluctuations and the Ginzburg criterion
25(1)
A standard exercise: the ferromagnetic Ising model
25(2)
Probability theory
27(12)
Basic notions
27(2)
Special probability distributions and the central limit theorem
29(1)
Statistical errors
30(1)
Markov chains and master equations
31(1)
The `art' of random number generation
32(7)
Non-equilibrium and dynamics: some introductory comments
39(9)
Physical applications of master equations
39(1)
Conservation laws and their consequences
40(3)
Critical slowing down at phase transitions
43(2)
Transport coefficients
45(1)
Concluding comments
45(1)
References
45(3)
Simple sampling Monte Carlo methods
48(20)
Introduction
48(1)
Comparisons of methods for numerical integration of given functions
48(3)
Simple methods
48(2)
Intelligent methods
50(1)
Boundary value problems
51(2)
Simulation of radioactive decay
53(1)
Simulation of transport properties
54(2)
Neutron transport
54(1)
Fluid flow
55(1)
The percolation problem
56(4)
Site percolation
56(3)
Cluster counting: the Hoshen--Kopelman algorithm
59(1)
Other percolation models
60(1)
Finding the groundstate of a Hamiltonian
60(1)
Generation of `random' walks
61(5)
Introduction
61(1)
Random walks
62(1)
Self-avoiding walks
63(2)
Growing walks and other models
65(1)
Final remarks
66(2)
References
66(2)
Importance sampling Monte Carlo methods
68(69)
Introduction
68(1)
The simplest case: single spin-flip sampling for the simple Ising model
69(36)
Algorithm
70(4)
Boundary conditions
74(3)
Finite size effects
77(13)
Finite sampling time effects
90(8)
Critical relaxation
98(7)
Other discrete variable models
105(10)
Ising models with competing interactions
105(4)
q-state Potts models
109(1)
Baxter and Baxter--Wu models
110(1)
Clock models
111(2)
Ising spin glass models
113(1)
Complex fluid models
114(1)
Spin-exchange sampling
115(5)
Constant magnetization simulations
115(1)
Phase separation
115(2)
Diffusion
117(3)
Hydrodynamic slowing down
120(1)
Microcanonical methods
120(2)
Demon algorithm
120(1)
Dynamic ensemble
121(1)
Q2R
121(1)
General remarks, choice of ensemble
122(1)
Statics and dynamics of polymer models on lattices
122(11)
Background
122(1)
Fixed bond length methods
123(1)
Bond fluctuation method
124(1)
Enhanced sampling using a fourth dimension
125(2)
The `wormhole algorithm' -- another method to equilibrate dense polymeric systems
127(1)
Polymers in solutions of variable quality: θ-point, collapse transition, unmixing
127(3)
Equilibrium polymers: a case study
130(3)
Some advice
133(4)
References
134(3)
More on importance sampling Monte Carlo methods for lattice systems
137(57)
Cluster flipping methods
137(7)
Fortuin--Kasteleyn theorem
137(1)
Swendsen--Wang method
138(3)
Wolff method
141(1)
`Improved estimators'
142(1)
Invaded cluster algorithm
142(1)
Probability changing cluster algorithm
143(1)
Specialized computational techniques
144(6)
Expanded ensemble methods
144(1)
Multispin coding
144(1)
N-fold way and extensions
145(3)
Hybrid algorithms
148(1)
Multigrid algorithms
148(1)
Monte Carlo on vector computers
148(1)
Monte Carlo on parallel computers
149(1)
Classical spin models
150(10)
Introduction
150(1)
Simple spin-flip method
151(2)
Heatbath method
153(1)
Low temperature techniques
153(1)
Over-relaxation methods
154(1)
Wolff embedding trick and cluster flipping
154(1)
Hybrid methods
155(1)
Monte Carlo dynamics vs. equation of motion dynamics
156(1)
Topological excitations and solitons
156(4)
Systems with quenched randomness
160(11)
General comments: averaging in random systems
160(3)
Parallel tempering: a general method to better equilibrate systems with complex energy landscapes
163(1)
Random fields and random bonds
164(1)
Spin glasses and optimization by simulated annealing
165(4)
Ageing in spin glasses and related systems
169(1)
Vector spin glasses: developments and surprises
170(1)
Models with mixed degrees of freedom: Si/Ge alloys, a case study
171(1)
Sampling the free energy and entropy
172(4)
Thermodynamic integration
172(2)
Groundstate free energy determination
174(1)
Estimation of intensive variables: the chemical potential
174(1)
Lee--Kosterlitz method
175(1)
Free energy from finite size dependence at Tc
175(1)
Miscellaneous topics
176(13)
Inhomogeneous systems: surfaces, interfaces, etc.
176(6)
Other Monte Carlo schemes
182(2)
Inverse Monte Carlo methods
184(1)
Finite size effects: a review and summary
185(1)
More about error estimation
186(1)
Random number generators revisited
187(2)
Summary and perspective
189(5)
References
190(4)
Off-lattice models
194(57)
Fluids
194(28)
NVT ensemble and the virial theorem
194(3)
NpT ensemble
197(4)
Grand canonical ensemble
201(4)
Near critical coexistence: a case study
205(2)
Subsystems: a case study
207(5)
Gibbs ensemble
212(3)
Widom particle insertion method and variants
215(2)
Monte Carlo Phase Switch
217(3)
Cluster algorithm for fluids
220(2)
`Short range' interactions
222(1)
Cutoffs
222(1)
Verlet tables and cell structure
222(1)
Minimum image convention
222(1)
Mixed degrees of freedom reconsidered
223(1)
Treatment of long range forces
223(3)
Reaction field method
223(1)
Ewald method
224(1)
Fast multipole method
225(1)
Absorbed monolayers
226(1)
Smooth substrates
226(1)
Periodic substrate potentials
226(1)
Complex fluids
227(4)
Application of the Liu-Luijten algorithm to a binary fluid mixture
230(1)
Polymers: an introduction
231(14)
Length scales and models
231(6)
Asymmetric polymer mixtures: a case study
237(3)
Applications: dynamics of polymer melts; thin adsorbed polymeric films
240(5)
Configurational bias and `smart Monte Carlo'
245(6)
References
248(3)
Reweighting methods
251(26)
Background
251(3)
Distribution functions
251(1)
Umbrella sampling
251(3)
Single histogram method: the Ising model as a case study
254(7)
Multi-histogram method
261(1)
Broad histogram method
262(1)
Transition matrix Monte Carlo
262(1)
Multicanonical sampling
263(5)
The multicanonical approach and its relationship to canonical sampling
263(1)
Near first order transitions
264(2)
Groundstates in complicated energy landscapes
266(1)
Interface free energy estimation
267(1)
A case study: the Casimir effect in critical systems
268(2)
`Wang-Landau sampling'
270(3)
A case study: evaporation/condensation transition of droplets
273(4)
References
274(3)
Quantum Monte Carlo methods
277(38)
Introduction
277(2)
Feynman path integral formulation
279(9)
Off-lattice problems: low-temperature properties of crystals
279(6)
Bose statistics and superfluidity
285(1)
Path integral formulation for rotational degrees of freedom
286(2)
Lattice problems
288(19)
The Ising model in a transverse field
288(2)
Anisotropic Heisenberg chain
290(3)
Fermions on a lattice
293(3)
An intermezzo: the minus sign problem
296(2)
Spinless fermions revisited
298(3)
Cluster methods for quantum lattice models
301(1)
Continuous time simulations
302(1)
Decoupled cell method
302(1)
Handscomb's method
303(1)
Wang-Landau sampling for quantum models
304(2)
Fermion determinants
306(1)
Monte Carlo methods for the study of groundstate properties
307(4)
Variational Monte Carlo (VMC)
308(1)
Green's function Monte Carlo methods (GFMC)
309(2)
Concluding remarks
311(4)
References
312(3)
Monte Carlo renormalization group methods
315(13)
Introduction to renormalization group theory
315(4)
Real space renormalization group
319(1)
Monte Carlo renormalization group
320(8)
Large cell renormalization
320(2)
Ma's method: finding critical exponents and the fixed point Hamiltonian
322(1)
Swendsen's method
323(2)
Location of phase boundaries
325(1)
Dynamic problems: matching time-dependent correlation functions
326(1)
Inverse Monte Carlo renormalization group transformations
327(1)
References
327(1)
Non-equilibrium and irreversible processes
328(22)
Introduction and perspective
328(1)
Driven diffusive systems (driven lattice gases)
328(3)
Crystal growth
331(2)
Domain growth
333(3)
Polymer growth
336(1)
Linear polymers
336(1)
Gelation
336(1)
Growth of structures and patterns
337(5)
Eden model of cluster growth
337(1)
Diffusion limited aggregation
338(2)
Cluster--cluster aggregation
340(1)
Cellular automata
340(2)
Models for film growth
342(5)
Background
342(1)
Ballistic deposition
343(1)
Sedimentation
343(1)
Kinetic Monte Carlo and MBE growth
344(3)
Transition path sampling
347(1)
Outlook: variations on a theme
348(2)
References
348(2)
Lattice gauge models: a brief introduction
350(13)
Introduction: gauge invariance and lattice gauge theory
350(2)
Some technical matters
352(1)
Results for Z(N) lattice gauge models
352(1)
Compact U(1) gauge theory
353(1)
SU(2) lattice gauge theory
354(1)
Introduction: quantum chromodynamics (QCD) and phase transitions of nuclear matter
355(2)
The deconfinement transition of QCD
357(3)
Where are we now?
360(3)
References
362(1)
A brief review of other methods of computer simulation
363(20)
Introduction
363(1)
Molecular dynamics
363(9)
Integration methods (microcanonical ensemble)
363(4)
Other ensembles (constant temperature, constant pressure, etc.)
367(3)
Non-equilibrium molecular dynamics
370(1)
Hybrid methods (MD + MC)
370(1)
Ab initio molecular dynamics
371(1)
Quasi-classical spin dynamics
372(3)
Langevin equations and variations (cell dynamics)
375(1)
Micromagnetics
376(1)
Dissipative particle dynamics (DPPD)
377(1)
Lattice gas cellular automata
378(1)
Lattice Boltzmann Equation
379(1)
Multiscale simulation
379(4)
References
381(2)
Monte Carlo methods outside of physics
383(10)
Commentary
383(1)
Protein folding
383(4)
Introduction
383(1)
Generalized ensemble methods
384(2)
Globular proteins: a case study
386(1)
`Biologically inspired physics'
387(1)
Mathematics/statistics
388(1)
Sociophysics
388(1)
Econophysics
388(1)
`Traffic' simulations
389(2)
Medicine
391(2)
References
392(1)
Outlook
393(2)
Appendix: listing of programs mentioned in the text 395(32)
Index 427

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