評論(0

統計物理中的蒙特卡羅方法

標籤: 暫無標籤

1 統計物理中的蒙特卡羅方法 -圖書信息

  出版社: 世界圖書出版公司北京公司; 第1版 (2008年5月1日)

  外文書名: A Guide to Monte Carlo Simulations in Statistical Physics 2nd Ed

  平裝: 432頁

  正文語種: 英語

  開本: 16

  ISBN: 7506292106, 9787506292108

  條形碼: 9787506292108

  尺寸: 25.8 x 18.2 x 2 cm

  重量: 739 g

2 統計物理中的蒙特卡羅方法 -作者簡介

  作者:(美國)蘭道(David P.Landau & Kurt Binder)

3 統計物理中的蒙特卡羅方法 -內容簡介

  《統計物理中的蒙特卡羅方法(第2版)》主要內容: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.

4 統計物理中的蒙特卡羅方法 -目錄

  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

上一篇[轉注古音略]    下一篇 [綠野平疇]

相關評論

同義詞:暫無同義詞