图书信息

作者简介

内容简介

目录

图书信息

出版社: 世界图书出版公司北京公司; 第1版 (2008年5月1日)

外文书名: A Guide to Monte Carlo Simulations in Statistical Physics 2nd Ed

平装: 432页

正文语种: 英语

开本: 16

ISBN: 7506292106, 9787506292108

条形码: 9787506292108

尺寸: 25.8 x 18.2 x 2 cm

重量: 739 g

作者简介

作者：(美国)兰道(David P.Landau & Kurt Binder)

内容简介

《统计物理中的蒙特卡罗方法(第2版)》主要内容：This new and updated deals with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics as well as in related fields, for example polymer science, lattice gauge theory and protein folding.

After briefly recalling essential background in statistical mechanics and probability theory, the authors give a succinct overview of simple sampling methods. The next several chapters develop the importance sampling method, both for lattice models and for systems in continuum space. The concepts behind the various simulation algorithms are explained in a comprehensive fashion, as are the techniques for efficient evaluation of system configurations generated by simulation (histogram extrapolation, multicanonicai sampling, Wang-Landau sampling, thermodynamic integration and so forth). The fact that simulations deal with small systems is emphasized. The text incorporates various finite size scaling concepts to show how a careful analysis of finite size effects can be a useful tool for the analysis of simulation results. Other chapters also provide introductions to quantum Monte Carlo methods, aspects of simulations of growth phenomena and other systems far from equilibrium, and the Monte Carlo Renormalization Group approach to critical phenomena. A brief overview of other methods of computer simulation is given, as is an outlook for the use of Monte Carlo simulations in disciplines outside of physics. Many applications, examples and exercises are provided throughout the book. Furthermore, many new references have been added to highlight both the recent technical advances and the key applications that they now make possible.

This is an excellent guide for graduate students who have to deal with computer simulations in their research, as well as postdoctoral researchers, in both physics and physical chemistry. It can be used as a textbook for graduate courses on computer simulations in physics and related disciplines.

目录

Preface

1 Introduction

1.1 What is a Monte Carlo simulation

1.2 What problems can we solve with it

1.3 What difficulties will we encounter

1.3.1 Limited computer time and memory

1.3.2 Statistical and other errors

1.4 What strategy should we follow in approaching a problem

1.5 How do simulations relate to theory and experiment

1.6 Perspective

2 Some necessary background

2.1 Thermodynamics and statistical mechanics: a quick reminder

2.1.1 Basic notions

2.1.2 Phase transitions

2.1.3 Ergodicity and broken symmetry

2.1.4 Fluctuations and the Ginzburg criterion

2.1.5 A standard exercise: the ferromagnetic Ising model

2.2 Probability theory

2.2.1 Basic notions

2.2.2 Special probability distributions and the central limit theorem

2.2.3 Statistical errors

2.2.4 Markov chains and master equations

2.2.5 The 'art' of random number generation

2.3 Non-equilibrium and dynamics: some introductory comments

2.3.1 Physical applications of master equations

2.3.2 Conservation laws and their consequences

2.3.3 Critical slowing down at phase transitions

2.3.4 Transport coefficients

2.3.5 Concluding comments

References

3 Simple sampling Monte Carlo methods

3.1 Introduction

3.2 Comparisons of methods for numerical integration of given

functions

3.2.1 Simple methods

3.2.2 Intelligent methods

3.3 Boundary value problems

3.4 Simulation of radioactive decay

3.5 Simulation of transp6rt properties

3.5.1 Neutron transport

3.5.2 Fluid flow

3.6 The percolation problem

3.6.1 Site percolation

3.6.2 Cluster counting: the Hoshen-Kopelman algorithm

3.6.3 Other percolation models

3.7 Finding the groundstate of a Hamiltonian

3.8 Generation of 'random' walks

3.8.1 Introduction

3.8.2 Random walks

3.8.3 Self-avoiding walks

3.8.4 Growing walks and other models

3.9 Final remarks

References

4 Importance sampling Monte Carlo methods

4.1 Introduction

4.2 The simplest case: single spin-flip sampling for the simple Ising model

4.2.1 Algorithm

4.2.2 Boundary conditions

4.2.3 Finite size effects

4.2.4 Finite sampling time effects

4.2.5 Critical relaxation

4.3 Other discrete variable models

4.3.1 Ising models with competing interactions

4.3.2 q-state Potts models

4.3.3 Baxter and Baxter-Wu models

4.3.4 Clock models

4.3.5 Ising spin glass models

4.3.6 Complex fluid models

4.4 Spin-exchange sampling

4.4.1 Constant magnetization simulations

4.4.2 Phase separation

4.4.3 Diffusion

4.4.4 Hydrodynamic slowing down

4.5 Microcanonical methods

4.5.1 Demon algorithm

4.5.2 Dynamic ensemble

4.5.3 Q2R

4.6 General remarks, choice of ensemble

4.7 Statics and dynamics of polymer models on lattices

4.7.1 Background

4.7.2 Fixed bond length methods

4.7.3 Bond fluctuation method

4.7.4 Enhanced sampling using a fourth dimension

4.7.5 The 'wormhole algorithm' - another method to equilibrate dense polymeric systems

4.7.6 Polymers in solutions of variable quality: 0-point, collapse transition, unmixing

4.7.7 Equilibrium polymers: a case study

4.8 Some advice

References

5 More on importance sampling Monte Carlo methods for lattice systems

5.1 Cluster flipping methods

5.1.1 Fortuin-Kasteleyn theorem

5.1.2 Swendsen-Wang method

5.1.3 Wolff method

5.1.4 'Improved estimators'

5.1.5 Invaded cluster algorithm

5.1.6 Probability changing cluster algorithm

5.2 Specialized computational techniques

5.2.1 Expanded ensemble methods

5.2.2 Multispin coding

5.2.3 N-fold way and extensions

5.2.4 Hybrid algorithms

5.2.5 Multigrid algorithms

5.2.6 Monte Carlo on vector computers

5.2.7 Monte Carlo on parallel computers

5.3 Classical spin models

5.3.1 Introduction

5.3.2 Simple spin-flip method

5.3.3 Heatbath method

5.3.4 Low temperature techniques

5.3.5 Over-relaxation methods

5.3.6 Wolff embedding trick and cluster flipping

5.3.7 Hybrid methods

5.3.8 Monte Carlo dynamics vs. equation of motion dynamics

5.3.9 Topological excitations and solitons

5.4 Systems with quenched randomness

5.4.1 General comments: averaging in random systems

5.4.2 Parallel tempering: a general method to better equilibrate systems with complex energy landscapes

5.4.3 Random fields and random bonds

5.4.4 Spin glasses and optimization by simulated annealing

5.4.5 Ageing in spin glasses and related systems

5.4.6 Vector spin glasses: developments and surprises

5.5 Models with mixed degrees of freedom: Si/Ge alloys, a case study

5.6 Sampling the free energy and entropy

5.6.1 Thermodynamic integration

5.6.2 Groundstate free energy determination

5.6.3 Estimation of intensive variables: the chemical potential

5.6.4 Lee-Kosterlitz method

5.6.5 Free energy from finite size dependence at Tc

5.7 Miscellaneous topics

5.7.1 Inhomogeneous systems: surfaces, interfaces, etc.

5.7.2 Other Monte Carlo schemes

5.7.3 Inverse Monte Carlo methods

5.7.4 Finite size effects: a review and summary

5.7.5 More about error estimation

5.7.6 Random number generators revisited

5.8 Summary and perspective

References

6 Off-lattice models

6.1 Fluids

6.1.1 NVT ensemble and the virial theorem

6.1.2 NpT ensemble

6.1.3 Grand canonical ensemble

6.1.4 Near critical coexistence: a case study

6.1.5 Subsystems: a case study

6.1.6 Gibbs ensemble

6.1.7 Widom particle insertion method and variants

6.1.8 Monte Carlo Phase Switch

6.1.9 Cluster algorithm for fluids

6.2 'Short range' interactions

6.2.1 Cutoffs

6.2.2 Verlet tables and cell structure

6.2.3 Minimum image convention

6.2.4 Mixed degrees of freedom reconsidered

6.3 Treatment of long range forces

6.3.1 Reaction field method

6.3.2 Ewald method

6.3.3 Fast multipole method

6.4 Adsorbed monolayers

6.4.1 Smooth substrates

6.4.2 Periodic substrate potentials

6.5 Complex fluids

6.5.1 Application of the Liu-Luijten algorithm to a binary fluid mixture

6.6 Polymers: an introduction

6.6.1 Length scales and models

6.6.2 Asymmetric polymer mixtures: a case study

6.6.3 Applications: dynamics of polymer melts; thin adsorbed polymeric films

6.7 Configurational bias and 'smart Monte Carlo'

References

7 Reweighting methods

7.1 Background

7.1.1 Distribution functions

7.1.2 Umbrella sampling

7.2 Single histogram method: the Ising model as a case study

7.3 Multi-histogram method

7.4 Broad histogram method

7.5 Transition matrix Monte Carlo

7.6 Multicanonical sampling

7.6.1 The multicanonical approach and its relationship to canonical sampling

7.6.2 Near first order transitions

7.6.3 Groundstates in complicated energy landscapes

7.6.4 Interface free energy estimation

7.7 A case study: the Casimir effect in critical systems

7.8 'Wang-Landau sampling'

7.9 A case study: evaporation/condensation transition of droplets

References

8 Quantum Monte Carlo methods

8.1 Introduction

8.2 Feynman path integral formulation

8.2.1 Off-lattice problems: low-temperature properties of crystals

8.2.2 Bose statistics and superfluidity

8.2.3 Path integral formulation for rotational degrees of freedom

8.3 Lattice problems

8.3.1 The Ising model in a transverse field

8.3.2 Anisotropic Heisenberg chain

8.3.3 Fermions on a lattice

8.3.4 An intermezzo: the minus sign problem

8.3.5 Spinless fermions revisited

8.3.6 Cluster methods for quantum lattice models

8.3.7 Continuous time simulations

8.3.8 Decoupled cell method

8.3.9 Handscomb's method

8.3.10 Wang-Landau sampling for quantum models

8.3.11 Fermion determinants

8.4 Monte Carlo methods for the study of groundstate properties

8.4.1 Variational Monte Carlo （VMC）

8.4.2 Green's function Monte Carlo methods （GFMC）

8.5 Concluding remarks

References

9 Monte Carlo renormalization group methods

9.1 Introduction to renormalization group theory

9.2 Real space renormalization group

9.3 Monte Carlo renormalization group

9.3.1 Large cell renormalization

9.3.2 Ma's method: finding critical exponents and the fixed point Hamiltonian

9.3.3 Swendsen's method

9.3.4 Location of phase boundaries

9.3.5 Dynamic problems: matching time-dependent correlation functions

9.3.6 Inverse Monte Carlo renormalization group transformations

References

10 Non-equilibrium and irreversible processes

10.1 Introduction and perspective

10.2 Driven diffusive systems （driven lattice gases）

10.3 Crystal growth

10.4 Domain growth

10.5 Polymer growth

10.5.1 Linear polymers

10.5.2 Gelation

10.6 Growth of structures and patterns

10.6.1 Eden model of cluster growth

10.6.2 Diffusion limited aggregation

10.6.3 Cluster-cluster aggregation

10.6.4 Cellular automata

10.7 Models for film growth

10.7.1 Background

10.7.2 Ballistic deposition

10.7.3 Sedimentation

10.7.4 Kinetic Monte Carlo and MBE growth

10.8 Transition path sampling

10.9 Outlook: variations on a theme

References

11 Lattice gauge models: a brief introduction

11.1 Introduction: gauge invariance and lattice gauge theory

11.2 Some technical matters

11.3 Results for Z（N） lattice gauge models

11.4 Compact U（1） gauge theory

11.5 SU（2） lattice gauge theory

11.6 Introduction: quantum chromodynamics （QCD） and phase transitions of nuclear matter

11.7 The deconfinement transition of QCD

11.8 Where are we now

References

12 A brief review of other methods of computer simulation

12.1 Introduction

12.2 Molecular dynamics

12.2.1 Integration methods （microcanonical ensemble）

12.2.2 Other ensembles （constant temperature, constant pressure,etc.）

12.2.3 Non-equilibrium molecular dynamics

12.2.4 Hybrid methods （MD + MC）

12.2.5 Ab initio molecular dynamics

12.3 Quasi-classical spin dynamics

12.4 Langevin equations and variations （cell dynamics）

12.5 Micromagnetics

12.6 Dissipative particle dynamics （DPPD）

12.7 Lattice gas cellular automata

12.8 Lattice Boltzmann Equation

12.9 Multiscale simulation

References

13 Monte Carlo methods outside of physics

13.1 Commentary

13.2 Protein folding

13.2.1 Introduction

13.2.2 Generalized ensemble methods

13.2.3 Globular proteins: a case study

13.3 'Biologically inspired physics'

13.4 Mathematics/statistics

13.5 Sociophysics

13.6 Econophysics

13.7 'Traffic' simulations

13.8 Medicine

References

14 Outlook

Appendix: listing of programs mentioned in the text

Index