查看完整版本: A Guide to Monte Carlo Simulations in Statistical Physics【Landau&Binder】

A Guide to Monte Carlo Simulations in Statistical Physics【Landau&Binder】

[书名]A Guide to Monte Carlo Simulations in Statistical Physics （已搜）
[作者]David P. Landau & Kurt Binder
[出版社]Cambridge University Press
[关键词] Monte Carlo
[内容简介]*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. (6.5 MB) 449 pages

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[ISBN号] 978-0521842389
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[url]http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521842387[/url]

A Guide to Monte Carlo Simulations in Statistical Physics 2nd Edition David P. Landau University of Georgia Kurt Binder
Johannes Gutenberg Universit?t Mainz, Germany
[img]http://assets.cambridge.org/97805218/42389/cover/9780521842389.jpg[/img]

Description:

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.

? A broad and self-contained overview of Monte Carlo simulations ? Contains extensive cross-referencing between
simulation and relevant theory and between applications of similar algorithms in different contexts ? Provides many
applications, examples, ‘recipes’, and specific case studies

Contents 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 method 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.

Reviews From the first edition: ‘This book will serve as a useful introduction to those entering the field, while for
those already versed in the subject it provides a timely survey of what has been achieved.’ Journal of Statistical
Physics

'... an excellent guide book...' Zentralblatt MATH

Table of Contents: [url]http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521842389&ss=toc[/url]
PDF文件：[url]http://assets.cambridge.org/97805218/42389/toc/9780521842389_toc.pdf[/url]

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Contents

Preface xii
1 Introduction 1
1.1 What is a Monte Carlo simulation? 1
1.2 What problems can we solve with it? 2
1.3 What difficulties will we encounter? 3
1.3.1 Limited computer time and memory 3
1.3.2 Statistical and other errors 3
1.4 What strategy should we follow in approaching a problem? 4
1.5 How do simulations relate to theory and experiment? 4
1.6 Perspective 6
2 Some necessary background 7
2.1 Thermodynamics and statistical mechanics: a quick reminder 7
2.1.1 Basic notions 7
2.1.2 Phase transitions 13
2.1.3 Ergodicity and broken symmetry 24
2.1.4 Fluctuations and the Ginzburg criterion 25
2.1.5 A standard exercise: the ferromagnetic Ising model 25
2.2 Probability theory 27
2.2.1 Basic notions 27
2.2.2 Special probability distributions and the central limit theorem 29
2.2.3 Statistical errors 30
2.2.4 Markovch ains and master equations 31
2.2.5 The ‘art’ of random number generation 32
2.3 Non-equilibrium and dynamics: some introductory comments 39
2.3.1 Physical applications of master equations 39
2.3.2 Conservation laws and their consequences 40
2.3.3 Critical slowing down at phase transitions 43
2.3.4 Transport coefficients 45
2.3.5 Concluding comments 45
References 45
3 Simple sampling Monte Carlo methods 48
3.1 Introduction 48
3.2 Comparisons of methods for numerical integration of given functions 48
3.2.1 Simple methods 48
3.2.2 Intelligent methods 50
3.3 Boundary value problems 51
3.4 Simulation of radioactive decay 53
3.5 Simulation of transport properties 54
3.5.1 Neutron transport 54
3.5.2 Fluid flow 55
3.6 The percolation problem 56
3.6.1 Site percolation 56
3.6.2 Cluster counting: the Hoshen–Kopelman algorithm 59
3.6.3 Other percolation models 60
3.7 Finding the groundstate of a Hamiltonian 60
3.8 Generation of ‘random’ walks 61
3.8.1 Introduction 61
3.8.2 Random walks 62
3.8.3 Self-avoiding walks 63
3.8.4 Growing walks and other models 65
3.9 Final remarks 66
References 66
4 Importance sampling Monte Carlo methods 68
4.1 Introduction 68
4.2 The simplest case: single spin-flip sampling for the simple Ising model 69
4.2.1 Algorithm 70
4.2.2 Boundary conditions 74
4.2.3 Finite size effects 77
4.2.4 Finite sampling time effects 90
4.2.5 Critical relaxation 98
4.3 Other discrete variable models 105
4.3.1 Ising models with competing interactions 105
4.3.2 q-state Potts models 109
4.3.3 Baxter and Baxter–Wu models 110
4.3.4 Clock models 111
4.3.5 Ising spin glass models 113
4.3.6 Complex fluid models 114
4.4 Spin-exchange sampling 115
4.4.1 Constant magnetization simulations 115
4.4.2 Phase separation 115
4.4.3 Diffusion 117
4.4.4 Hydrodynamic slowing down 120
4.5 Microcanonical methods 120
4.5.1 Demon algorithm 120
4.5.2 Dynamic ensemble 121
4.5.3 Q2R 121
4.6 General remarks, choice of ensemble 122
4.7 Statics and dynamics of polymer models on lattices 122
4.7.1 Background 122
4.7.2 Fixed bond length methods 123
4.7.3 Bond fluctuation method 124
4.7.4 Enhanced sampling using a fourth dimension 125
4.7.5 The ‘wormhole algorithm’ – another method to equilibrate dense polymeric systems 127
4.7.6 Polymers in solutions of variable quality: Gamma-point, collapse transition, unmixing 127
4.7.7 Equilibrium polymers: a case study 130
4.8 Some advice 133
References 134
5 More on importance sampling Monte Carlo methods for lattice systems 137
5.1 Cluster flipping methods 137
5.1.1 Fortuin–Kasteleyn theorem 137
5.1.2 Swendsen–Wang method 138
5.1.3 Wolff method 141
5.1.4 ‘Improved estimators’ 142
5.1.5 Invaded cluster algorithm 142
5.1.6 Probability changing cluster algorithm 143
5.2 Specialized computational techniques 144
5.2.1 Expanded ensemble methods 144
5.2.2 Multispin coding 144
5.2.3 N-fold way and extensions 145
5.2.4 Hybrid algorithms 148
5.2.5 Multigrid algorithms 148
5.2.6 Monte Carlo on vector computers 148
5.2.7 Monte Carlo on parallel computers 149
5.3 Classical spin models 150
5.3.1 Introduction 150
5.3.2 Simple spin-flip method 151
5.3.3 Heatbath method 153
5.3.4 Low temperature techniques 153
5.3.5 Over-relaxation methods 154
5.3.6 Wolff embedding trick and cluster flipping 154
5.3.7 Hybrid methods 155
5.3.8 Monte Carlo dynamics vs. equation of motion dynamics 156
5.3.9 Topological excitations and solitons 156
5.4 Systems with quenched randomness 160
5.4.1 General comments: averaging in random systems 160
5.4.2 Parallel tempering: a general method to better equilibrate systems with complex energy landscapes 163
5.4.3 Random fields and random bonds 164
5.4.4 Spin glasses and optimization by simulated annealing 165
5.4.5 Ageing in spin glasses and related systems 169
5.4.6 Vector spin glasses: developments and surprises 170
5.5 Models with mixed degrees of freedom: Si/Ge alloys, a case study 171
5.6 Sampling the free energy and entropy 172
5.6.1 Thermodynamic integration 172
5.6.2 Groundstate free energy determination 174
5.6.3 Estimation of intensive variables: the chemical potential 174
5.6.4 Lee–Kosterlitz method 175
5.6.5 Free energy from finite size dependence at Tc 175
5.7 Miscellaneous topics 176
5.7.1 Inhomogeneous systems: surfaces, interfaces, etc. 176
5.7.2 Other Monte Carlo schemes 182
5.7.3 Inverse Monte Carlo methods 184
5.7.4 Finite size effects: a review and summary 185
5.7.5 More about error estimation 186
5.7.6 Random number generators revisited 187
5.8 Summary and perspective 189
References 190
6 Off-lattice models 194
6.1 Fluids 194
6.1.1 NVT ensemble and the virial theorem 194
6.1.2 NpT ensemble 197
6.1.3 Grand canonical ensemble 201
6.1.4 Near critical coexistence: a case study 205
6.1.5 Subsystems: a case study 207
6.1.6 Gibbs ensemble 212
6.1.7 Widom particle insertion method and variants 215
6.1.8 Monte Carlo Phase Switch 217
6.1.9 Cluster algorithm for fluids 220
6.2 ‘Short range’ interactions 222
6.2.1 Cutoffs 222
6.2.2 Verlet tables and cell structure 222
6.2.3 Minimum image convention 222
6.2.4 Mixed degrees of freedom reconsidered 223
6.3 Treatment of long range forces 223
6.3.1 Reaction field method 223
6.3.2 Ewald method 224
6.3.3 Fast multipole method 225
6.4 Adsorbed monolayers 226
6.4.1 Smooth substrates 226
6.4.2 Periodic substrate potentials 226
6.5 Complex fluids 227
6.5.1 Application of the Liu-Luijten algorithm to a binary fluid mixture 230
6.6 Polymers: an introduction 231
6.6.1 Length scales and models 231
6.6.2 Asymmetric polymer mixtures: a case study 237
6.6.3 Applications: dynamics of polymer melts; thin adsorbed polymeric films 240
6.7 Configurational bias and ‘smart Monte Carlo’ 245
References 248
7 Reweigh ting methods 251
7.1 Background 251
7.1.1 Distribution functions 251
7.1.2 Umbrella sampling 251
7.2 Single histogram method: the Ising model as a case study 254
7.3 Multi-histogram method 261
7.4 Broad histogram method 262
7.5 Transition matrix Monte Carlo 262
7.6 Multicanonical sampling 263
7.6.1 The multicanonical approach and its relationship to canonical sampling 263
7.6.2 Near first order transitions 264
7.6.3 Groundstates in complicated energy landscapes 266
7.6.4 Interface free energy estimation 267
7.7 A case study: the Casimir effect in critical systems 268
7.8 ‘Wang-Landau sampling’ 270
7.9 A case study: evaporation/condensation transition of droplets 273
References 274
8 Quantum Monte Carlo methods 277
8.1 Introduction 277
8.2 Feynman path integral formulation 279
8.2.1 Off-lattice problems: low-temperature properties of crystals 279
8.2.2 Bose statistics and superfluidity 285
8.2.3 Path integral formulation for rotational degrees of freedom 286
8.3 Lattice problems 288
8.3.1 The Ising model in a transverse field 288
8.3.10 Wang-Landau sampling for quantum models 304
8.3.11 Fermion determinants 306
8.3.2 Anisotropic Heisenberg chain 290
8.3.3 Fermions on a lattice 293
8.3.4 An intermezzo: the minus sign problem 296
8.3.5 Spinless fermions revisited 298
8.3.6 Cluster methods for quantum lattice models 301
8.3.7 Continuous time simulations 302
8.3.8 Decoupled cell method 302
8.3.9 Handscomb’s method 303
8.4 Monte Carlo methods for the study of groundstate properties 307
8.4.1 Variational Monte Carlo (VMC) 308
8.4.2 Green’s function Monte Carlo methods (GFMC) 309
8.5 Concluding remarks 311
References 312
9 Monte Carlo renormalization group methods 315
9.1 Introduction to renormalization group theory 315
9.2 Real space renormalization group 319
9.3 Monte Carlo renormalization group 320
9.3.1 Large cell renormalization 320
9.3.2 Ma’s method: finding critical exponents and the fixed point Hamiltonian 322
9.3.3 Swendsen’s method 323
9.3.4 Location of phase boundaries 325
9.3.5 Dynamic problems: matching time-dependent correlation functions 326
9.3.6 Inverse Monte Carlo renormalization group transformations 327
References 327
10 Non-equilibrium and irreversible processes 328
10.1 Introduction and perspective 328
10.2 Driven diffusive systems (driven lattice gases) 328
10.3 Crystal growth 331
10.4 Domain growth 333
10.5 Polymer growth 336
10.5.1 Linear polymers 336
10.5.2 Gelation 336
10.6 Growth of structures and patterns 337
10.6.1 Eden model of cluster growth 337
10.6.2 Diffusion limited aggregation 338
10.6.3 Cluster–cluster aggregation 340
10.6.4 Cellular automata 340
10.7 Models for film growth 342
10.7.1 Background 342
10.7.2 Ballistic deposition 343
10.7.3 Sedimentation 343
10.7.4 Kinetic Monte Carlo and MBE growth 344
10.8 Transition path sampling 347
10.9 Outlook: variations on a theme 348
References 348
11 Lattice gauge models: a brief introduction 350
11.1 Introduction: gauge invariance and lattice gauge theory 350
11.2 Some technical matters 352
11.3 Results for Z(N) lattice gauge models 352
11.4 Compact U(1) gauge theory 353
11.5 SU(2) lattice gauge theory 354
11.6 Introduction: quantum chromodynamics (QCD) and phase transitions of nuclear matter 355
11.7 The deconfinement transition of QCD 357
11.8 Where are we now? 360
References 362
12 A brief review of other methods of computer simulation 363
12.1 Introduction 363
12.2 Molecular dynamics 363
12.2.1 Integration methods (microcanonical ensemble) 363
12.2.2 Other ensembles (constant temperature, constant pressure, etc.) 367
12.2.3 Non-equilibrium molecular dynamics 370
12.2.4 Hybrid methods (MD + MC) 370
12.2.5 Ab initio molecular dynamics 371
12.3 Quasi-classical spin dynamics 372
12.4 Langevin equations and variations (cell dynamics) 375
12.5 Micromagnetics 376
12.6 Dissipative particle dynamics (DPPD) 377
12.7 Lattice gas cellular automata 378
12.8 Lattice Boltzmann Equation 379
12.9 Multiscale simulation 379
References 381
13 Monte Carlo methods outside of physics 383
13.1 Commentary 383
13.2 Protein folding 383
13.2.1 Introduction 383
13.2.2 Generalized ensemble methods 384
13.2.3 Globular proteins: a case study 386
13.3 ‘Biologically inspired physics’ 387
13.4 Mathematics/statistics 388
13.5 Sociophysics 388
13.6 Econophysics 388
13.7 ‘Traffic’ simulations 389
13.8 Medicine 391
References 392
14 Outlook 393
Appendix: listing of programs mentioned in the text 395
Index 427

[url]http://bbs.matwav.com/post/view?bid=57&id=593756[/url]
主要責任者 Landau, David P
题名 A guide to Monte Carlo simulations in statistical physics / David P. Landau, Kurt Binder
出版发行 Cambridge ; New York : Cambridge University Press, c2000
Preface
Index 379
1 Introduction 1
2 Some necessary background 7
3 Simple sampling Monte Carlo methods 48
4 Importance sampling Monte Carlo methods 68
5 More on importance sampling Monte Carlo methods for lattice systems 133
6 Off-lattice models 182
7 Reweighting methods 230
8 Quantum Monte Carlo methods 250
9 Monte Carlo renormalization group methods 286
10 Non-equilibrium and irreversible processes 299
11 Lattice gauge models: a brief introduction 320
12 A brief review of other methods of computer simulation 332
13 Outlook 346
App.: listing of programs mentioned in the text 348
A Guide to Monte Carlo Simulations in Statistical Physics(Cambridge2000).pdf
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本书是一部详述了在凝聚态物理学、统计力学及相关领域中遇到的复物理系统蒙特卡罗模拟的各个方面，书中各章有应用实例、例题、思考题和习题，以便于读者深刻理解书中所述内容。本书可作为物理学中的计算模拟研究生教科书。
目次：导论；基础理论；简单抽样蒙特卡罗方法；重要抽样蒙特卡罗方法；格点系统用的重要抽样蒙特卡罗方法；偏格点模型；重权（reweighting）方法；量子蒙特卡罗方法；蒙特卡罗重正化群方法；非平衡不可逆过程；点规模型简介；其它计算机模拟方法综述。
读者对象：物理学和物理化学专业的研究生及研究人员。