A guide to Monte Carlo simulations in statistical physics:
Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This fourth edition contains extensive new material describing numerous powerful al...
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Cambridge University Press
2021
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| Zusammenfassung: | Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This fourth edition contains extensive new material describing numerous powerful algorithms not covered in previous editions, in some cases representing new developments that have only recently appeared. Older methodologies whose impact was previously unclear or unappreciated are also introduced, in addition to many small revisions that bring the text and cited literature up to date. This edition also introduces the use of petascale computing facilities in the Monte Carlo arena. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory |
| Beschreibung: | xvii, 564 Seiten Illustrationen, Diagramme |
| ISBN: | 9781108490146 |
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| 100 | 1 | |a Landau, David P. |d 1941- |e Verfasser |0 (DE-588)131584960 |4 aut | |
| 245 | 1 | 0 | |a A guide to Monte Carlo simulations in statistical physics |c David P. Landau, Center for Simulational Physics, University of Georgia, USA, Kurt Binder, Institut für Physik, Johannes-Gutenberg-Universität, Germany |
| 250 | |a Fifth edition | ||
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| 520 | |a Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This fourth edition contains extensive new material describing numerous powerful algorithms not covered in previous editions, in some cases representing new developments that have only recently appeared. Older methodologies whose impact was previously unclear or unappreciated are also introduced, in addition to many small revisions that bring the text and cited literature up to date. This edition also introduces the use of petascale computing facilities in the Monte Carlo arena. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory | ||
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Datensatz im Suchindex
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| adam_text | Contents page Preface 1 Introduction 1.1 What is a Monte Carlo simulation? 1.2 A comment on the history of Monte Carlo simulations 1.3 What problems can we solve with it? 1.4 What difficulties will we encounter? 1.4.1 Limited computer time and memory 1.4.2 Statistical and other errors 1.4.3 Knowledge that every practitioner should have 1.5 What strategy should we follow in approaching a problem? 1.6 How do simulations relate to theory and experiment? 1.7 Perspective References 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 2.3 The ‘art’ of random number generation 2.3.1 Background 2.3.2 Congruential method 2.3.3 Mixed congruential methods 2.3.4 Shift register algorithm 2.3.5 Lagged Fibonacci methods 2.3.6 Tests for quality 2.3.7 Non-uniform distributions xv 1 1 2 3 4 4 4 5 5 6 7 8 9 9 9 17 29 30 31 32 32 34 35 36 38 38 39 40 40 41 41 44 v
vi Contents 2.4 Non-equilibrium and dynamics: someintroductory comments 2.4.1 Physical applications of masterequations 2.4.2 Conservation laws and their consequences 2.4.3 Critical slowing down at phase transitions 2.4.4 Transport coefficients 2.4.5 Concluding comments: why bother about dynamics when doing Monte Carlo for statics? 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 transport 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 3.6.4 The Lorentz gas and cherry pit models and the localization transition 3.6.5 Explosive percolation 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 44 44 46 49 51 51 52 54 54 54 54 56 57 59 60 60 61 62 62 67 68 69 70 72 73 73 74 75 77 78 78 80 80 81 82 85 91 105 115 123 123
Contents 4.3.2 ø-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 4.4.5 Interface between coexisting phases 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 4.7.8 The pruned enriched Rosenbluth method (PERM): a biased sampling approach to simulate very long isolated chains 4.7.9 Perspective 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 Wolffmethod 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 TV-fold way and extensions vii 127 128 129 130 131 132 132 133 135 138 139 140 140 140 141 141 143 143 143 145 145 147 147 150 153 156 156 157 161 161 161 162 165 166 167 167 168 168 168 169
Contents 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-tilt 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 solitone 5.3.10 Finite size scaling for systems with vector order parameters 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 Aging İn spin glasses and related systems 5.4.6 Vector spin glasses: developments and surprises 5.4.7 The ground state of the Ising spin glass on the square lattice: a case study 5.5 Models with mixed degrees of freedom: Si/Ge alloys, a case study 5.6 Methods for systems with long range interactions 5.7 Parallel tempering, simulated tempering, and related methods: accuracy considerations 5.8 Sampling the free energy and entropy 5.8.1 Thermodynamic integration 5.8.2 Groundstate free energy determination 5.8.3 Estimation of intensive variables: the chemical potential 5.8.4 Lee-Kosterlitz method 5.8.5 Free energy from finite size dependence at TQ 5.9 Miscellaneous topics 5.9.1 Inhomogeneous systems: surfaces, interfaces, etc. 5.9.2 Anisotropic critical
phenomena: simulationboxes with arbitrary aspect ratio 5.9.3 Other Monte Carlo schemes 5.9.4 Inverse and reverse Monte Carlo methods 172 172 173 174 175 175 176 178 179 179 180 181 182 182 186 190 190 194 195 198 203 204 204 207 209 211 214 214 216 216 217 218 218 218 225 227 229
Contents 5.9.5 Finite size effects: review and summary 5.9.6 More about error estimation 5.9.7 Random number generators revisited 5.10 Summary and perspective References 6 Off-lattice models 6.1 Fluids 6.1.1 NVT ensemble and the viriai theorem 6.1.2 NpT ensemble 6.1.3 ‘Real’ microcanonical ensemble 6.1.4 Grand canonical ensemble 6.1.5 Near critical coexistence: a case study 6.1.6 Subsystems: a case study 6.1.7 Gibbs ensemble 6.1.8 Widom particle insertion method and variants 6.1.9 Monte Carlo phase switch 6.1.10 Cluster algorithm for fluids 6.1.11 Event chain algorithms 6.1.12 An extension of the ‘N-fold way’-algorithm to off-lattice systems 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 6.3.4 Particle-particle particle-mesh (P3M) method 6.4 Adsorbed monolayers 6.4.1 Smooth substrates 6.4.2 Periodic substrate potentials 6.5 Complex fluids 6.5.1 A case study: 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 6.6.4 Polymer melts: speeding up bond fluctuation model simulations 6.7 Liquid crystals; an introduction 6.8 Configurational bias and ‘smart Monte Carlo’ ix 231 231 233 237 237 243 243 243 247 251 252 256 258 264 266 269 273 274 277 278 278 278 279 279
280 280 280 281 282 283 283 283 285 288 289 289 296 298 303 305 309
x Contents 6.9 Estimation of excess free energies due to walls for fluids and solids 6.10 A symmetric, Lennard-Jones mixture: a case study 6.11 Finite size effects on interfacial properties: a case study 6.12 Outlook References 7 Reweighting methods 7.1 Background 7.1.1 Distribution functions 7.1.2 Umbrella sampling 7.2 Single histogram method 7.2.1 The Ising model as a case study 7.2.2 The surface-bulk multicritical point: another case study 7.3 Multihistogram 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 7.8.1 Basic algorithm 7.8.2 Applications to models with continuous variables 7.8.3 Two-dimensional Wang-Landau sampling: a case study 7.8.4 Microcanonical entropy inflection points 7.8.5 Back to numerical integration 7.8.6 Replica exchange Wang-Landau sampling 7.9 A case study: evaporation/condensation transition of droplets References 8 Quantum MonteCarlo 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 313 316 317 321 321 326 326 326 326 329 330 338 341 341 342 342 342 344 346 347 348 348 348
353 354 354 356 357 359 362 365 365 367 367 373 375 377 377
Contents 8.3.2 8.3.3 8.3.4 8.3.5 8.3.6 8.3.7 8.3.8 8.3.9 Anisotropic Heisenberg chain: an early case study Fermions on a lattice An intermezzo: the minus sign problem Spinless fermions revisited Cluster methods for quantum lattice models Continuous time simulations Decoupled cell method Handscomb’s method and the stochastic series expansion (SSE) approach 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 Quantum Monte Carlo in nuclear physics 8.6 Towards constructing the nodal surface of off-lattice, many-Fermion systems: the ‘survival of the fittest algorithm’ 8.7 Bypassing the minus sign problem: phase transitions in antiferromagnetic metals 8.8 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 10.2 10.3 10.4 Introduction and perspective Driven diffusive systems (driven lattice gases) Crystal growth Domain growth 10.4.1 Phase separation in mixtures 10.4.2 A case study: growth of domains and
aging phenomena in spin glasses xi 378 382 385 387 389 391 392 393 394 396 398 398 400 402 404 408 411 412 416 416 420 421 421 423 424 426 428 428 429 430 430 431 434 437 437 440
Contents 10.5 Polymer growth 10.5.1 Linear polymers 10.5.2 Kinetic gelation: a case study 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 MBEgrowth 10.8 Transition path sampling 10.8.1 What is transition path sampling? 10.8.2 A case study: the disk to slab transition in the two-dimensional Ising model 10.9 Forced polymer pore translocation: a case study 10.10 The Jarzynski non-equilibrium work theorem and its application to obtain free energy differences from trajectories 10.11 Outlook: variations on a theme References 11 Lattice gauge models:a brief introduction 11.1 11.2 11.3 11.4 11.5 11.6 Introduction: gauge invariance and lattice gauge theory Some technical matters Results for Z(N) lattice gauge models Compact U(l) gauge theory SU(2) lattice gauge theory Introduction: quantum chromodynamics (QCD) and phase transitions of nuclear matter 11.7 The deconfinement transition of QCD 11.8 Finite size scaling based on Polyakov loops: a case study 11.9 Towards quantitative predictions 11.10 Density of states in gauge theories 11.11 Perspective References 443 443 443 445 445 445 448 448 449 449 450 451 452 454 454 455 457 460 462 462 465 465 467 467 468 469 470 473 475 478 481 481 482 12 A brief reviewof other methodsof computer simulation 484 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) 484 484 484 488 491 491
Contents 12.2.5 Ab initio molecular dynamics 12.2.6 Hyperdynamies and metadynamics 12.2.7 Molecular dynamics for systems with open boundaries 12.3 Quasi-classical spin dynamics 12.3.1 Combined molecular dynamics-spin dynamics (MD-SD) simulations 12.4 Langevin equations and variations(cell dynamics) 12.5 Micromagnetics 12.6 Dissipative particle dynamics (DPD) 12.7 Lattice gas cellular automata 12.8 Lattice Boltzmann equation 12.9 Multiscale simulation 12.10 Multiparticle collision dynamics 12.11 Active matter 12.12 Machine learning References 13 Monte Carlo simulations at the periphery of physics and beyond 13.1 13.2 13.3 13.4 13.5 Commentary Astrophysics Materials science Chemistry ‘Biologically inspired’ physics 13.5.1 Commentary and perspective 13.5.2 Lattice proteins 13.5.3 Cell sorting 13.6 Biology 13.7 Mathematics/statistics/computerscience 13.8 Sociophysics 13.9 Econophysics 13.10 ‘Traffic’simulations 13.11 Medicine 13.12 Networks: what connections reallymatter? 13.13 Finance References 14 Monte Carlo studies of biological molecules 14.1 Introduction 14.2 Protein folding 14.2.1 Introduction 14.2.2 How to best simulate proteins: Monte Carlo or molecular dynamics 14.2.3 Generalized ensemble methods 14.2.4 Globular proteins: a case study 14.2.5 Simulations of membrane proteins xiii 492 493 494 495 499 500 501 502 503 504 505 507 509 512 515 519 519 519 520 522 524 524 524 527 527 529 530 530 531 533 534 535 536 540 540 541 541 542 543 545 545
XIV Contents 14.3 Monte Carlo simulations of RNA structures 14.4 Monte Carlo simulations of carbohydrates 14.5 Determining macromolecular structures 14.6 Outlook References 15 Emerging trends Index 548 549 551 551 552 554 556
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| adam_txt |
Contents page Preface 1 Introduction 1.1 What is a Monte Carlo simulation? 1.2 A comment on the history of Monte Carlo simulations 1.3 What problems can we solve with it? 1.4 What difficulties will we encounter? 1.4.1 Limited computer time and memory 1.4.2 Statistical and other errors 1.4.3 Knowledge that every practitioner should have 1.5 What strategy should we follow in approaching a problem? 1.6 How do simulations relate to theory and experiment? 1.7 Perspective References 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 2.3 The ‘art’ of random number generation 2.3.1 Background 2.3.2 Congruential method 2.3.3 Mixed congruential methods 2.3.4 Shift register algorithm 2.3.5 Lagged Fibonacci methods 2.3.6 Tests for quality 2.3.7 Non-uniform distributions xv 1 1 2 3 4 4 4 5 5 6 7 8 9 9 9 17 29 30 31 32 32 34 35 36 38 38 39 40 40 41 41 44 v
vi Contents 2.4 Non-equilibrium and dynamics: someintroductory comments 2.4.1 Physical applications of masterequations 2.4.2 Conservation laws and their consequences 2.4.3 Critical slowing down at phase transitions 2.4.4 Transport coefficients 2.4.5 Concluding comments: why bother about dynamics when doing Monte Carlo for statics? 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 transport 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 3.6.4 The Lorentz gas and cherry pit models and the localization transition 3.6.5 Explosive percolation 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 44 44 46 49 51 51 52 54 54 54 54 56 57 59 60 60 61 62 62 67 68 69 70 72 73 73 74 75 77 78 78 80 80 81 82 85 91 105 115 123 123
Contents 4.3.2 ø-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 4.4.5 Interface between coexisting phases 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 4.7.8 The pruned enriched Rosenbluth method (PERM): a biased sampling approach to simulate very long isolated chains 4.7.9 Perspective 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 Wolffmethod 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 TV-fold way and extensions vii 127 128 129 130 131 132 132 133 135 138 139 140 140 140 141 141 143 143 143 145 145 147 147 150 153 156 156 157 161 161 161 162 165 166 167 167 168 168 168 169
Contents 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-tilt 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 solitone 5.3.10 Finite size scaling for systems with vector order parameters 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 Aging İn spin glasses and related systems 5.4.6 Vector spin glasses: developments and surprises 5.4.7 The ground state of the Ising spin glass on the square lattice: a case study 5.5 Models with mixed degrees of freedom: Si/Ge alloys, a case study 5.6 Methods for systems with long range interactions 5.7 Parallel tempering, simulated tempering, and related methods: accuracy considerations 5.8 Sampling the free energy and entropy 5.8.1 Thermodynamic integration 5.8.2 Groundstate free energy determination 5.8.3 Estimation of intensive variables: the chemical potential 5.8.4 Lee-Kosterlitz method 5.8.5 Free energy from finite size dependence at TQ 5.9 Miscellaneous topics 5.9.1 Inhomogeneous systems: surfaces, interfaces, etc. 5.9.2 Anisotropic critical
phenomena: simulationboxes with arbitrary aspect ratio 5.9.3 Other Monte Carlo schemes 5.9.4 Inverse and reverse Monte Carlo methods 172 172 173 174 175 175 176 178 179 179 180 181 182 182 186 190 190 194 195 198 203 204 204 207 209 211 214 214 216 216 217 218 218 218 225 227 229
Contents 5.9.5 Finite size effects: review and summary 5.9.6 More about error estimation 5.9.7 Random number generators revisited 5.10 Summary and perspective References 6 Off-lattice models 6.1 Fluids 6.1.1 NVT ensemble and the viriai theorem 6.1.2 NpT ensemble 6.1.3 ‘Real’ microcanonical ensemble 6.1.4 Grand canonical ensemble 6.1.5 Near critical coexistence: a case study 6.1.6 Subsystems: a case study 6.1.7 Gibbs ensemble 6.1.8 Widom particle insertion method and variants 6.1.9 Monte Carlo phase switch 6.1.10 Cluster algorithm for fluids 6.1.11 Event chain algorithms 6.1.12 An extension of the ‘N-fold way’-algorithm to off-lattice systems 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 6.3.4 Particle-particle particle-mesh (P3M) method 6.4 Adsorbed monolayers 6.4.1 Smooth substrates 6.4.2 Periodic substrate potentials 6.5 Complex fluids 6.5.1 A case study: 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 6.6.4 Polymer melts: speeding up bond fluctuation model simulations 6.7 Liquid crystals; an introduction 6.8 Configurational bias and ‘smart Monte Carlo’ ix 231 231 233 237 237 243 243 243 247 251 252 256 258 264 266 269 273 274 277 278 278 278 279 279
280 280 280 281 282 283 283 283 285 288 289 289 296 298 303 305 309
x Contents 6.9 Estimation of excess free energies due to walls for fluids and solids 6.10 A symmetric, Lennard-Jones mixture: a case study 6.11 Finite size effects on interfacial properties: a case study 6.12 Outlook References 7 Reweighting methods 7.1 Background 7.1.1 Distribution functions 7.1.2 Umbrella sampling 7.2 Single histogram method 7.2.1 The Ising model as a case study 7.2.2 The surface-bulk multicritical point: another case study 7.3 Multihistogram 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 7.8.1 Basic algorithm 7.8.2 Applications to models with continuous variables 7.8.3 Two-dimensional Wang-Landau sampling: a case study 7.8.4 Microcanonical entropy inflection points 7.8.5 Back to numerical integration 7.8.6 Replica exchange Wang-Landau sampling 7.9 A case study: evaporation/condensation transition of droplets References 8 Quantum MonteCarlo 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 313 316 317 321 321 326 326 326 326 329 330 338 341 341 342 342 342 344 346 347 348 348 348
353 354 354 356 357 359 362 365 365 367 367 373 375 377 377
Contents 8.3.2 8.3.3 8.3.4 8.3.5 8.3.6 8.3.7 8.3.8 8.3.9 Anisotropic Heisenberg chain: an early case study Fermions on a lattice An intermezzo: the minus sign problem Spinless fermions revisited Cluster methods for quantum lattice models Continuous time simulations Decoupled cell method Handscomb’s method and the stochastic series expansion (SSE) approach 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 Quantum Monte Carlo in nuclear physics 8.6 Towards constructing the nodal surface of off-lattice, many-Fermion systems: the ‘survival of the fittest algorithm’ 8.7 Bypassing the minus sign problem: phase transitions in antiferromagnetic metals 8.8 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 10.2 10.3 10.4 Introduction and perspective Driven diffusive systems (driven lattice gases) Crystal growth Domain growth 10.4.1 Phase separation in mixtures 10.4.2 A case study: growth of domains and
aging phenomena in spin glasses xi 378 382 385 387 389 391 392 393 394 396 398 398 400 402 404 408 411 412 416 416 420 421 421 423 424 426 428 428 429 430 430 431 434 437 437 440
Contents 10.5 Polymer growth 10.5.1 Linear polymers 10.5.2 Kinetic gelation: a case study 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 MBEgrowth 10.8 Transition path sampling 10.8.1 What is transition path sampling? 10.8.2 A case study: the disk to slab transition in the two-dimensional Ising model 10.9 Forced polymer pore translocation: a case study 10.10 The Jarzynski non-equilibrium work theorem and its application to obtain free energy differences from trajectories 10.11 Outlook: variations on a theme References 11 Lattice gauge models:a brief introduction 11.1 11.2 11.3 11.4 11.5 11.6 Introduction: gauge invariance and lattice gauge theory Some technical matters Results for Z(N) lattice gauge models Compact U(l) gauge theory SU(2) lattice gauge theory Introduction: quantum chromodynamics (QCD) and phase transitions of nuclear matter 11.7 The deconfinement transition of QCD 11.8 Finite size scaling based on Polyakov loops: a case study 11.9 Towards quantitative predictions 11.10 Density of states in gauge theories 11.11 Perspective References 443 443 443 445 445 445 448 448 449 449 450 451 452 454 454 455 457 460 462 462 465 465 467 467 468 469 470 473 475 478 481 481 482 12 A brief reviewof other methodsof computer simulation 484 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) 484 484 484 488 491 491
Contents 12.2.5 Ab initio molecular dynamics 12.2.6 Hyperdynamies and metadynamics 12.2.7 Molecular dynamics for systems with open boundaries 12.3 Quasi-classical spin dynamics 12.3.1 Combined molecular dynamics-spin dynamics (MD-SD) simulations 12.4 Langevin equations and variations(cell dynamics) 12.5 Micromagnetics 12.6 Dissipative particle dynamics (DPD) 12.7 Lattice gas cellular automata 12.8 Lattice Boltzmann equation 12.9 Multiscale simulation 12.10 Multiparticle collision dynamics 12.11 Active matter 12.12 Machine learning References 13 Monte Carlo simulations at the periphery of physics and beyond 13.1 13.2 13.3 13.4 13.5 Commentary Astrophysics Materials science Chemistry ‘Biologically inspired’ physics 13.5.1 Commentary and perspective 13.5.2 Lattice proteins 13.5.3 Cell sorting 13.6 Biology 13.7 Mathematics/statistics/computerscience 13.8 Sociophysics 13.9 Econophysics 13.10 ‘Traffic’simulations 13.11 Medicine 13.12 Networks: what connections reallymatter? 13.13 Finance References 14 Monte Carlo studies of biological molecules 14.1 Introduction 14.2 Protein folding 14.2.1 Introduction 14.2.2 How to best simulate proteins: Monte Carlo or molecular dynamics 14.2.3 Generalized ensemble methods 14.2.4 Globular proteins: a case study 14.2.5 Simulations of membrane proteins xiii 492 493 494 495 499 500 501 502 503 504 505 507 509 512 515 519 519 519 520 522 524 524 524 527 527 529 530 530 531 533 534 535 536 540 540 541 541 542 543 545 545
XIV Contents 14.3 Monte Carlo simulations of RNA structures 14.4 Monte Carlo simulations of carbohydrates 14.5 Determining macromolecular structures 14.6 Outlook References 15 Emerging trends Index 548 549 551 551 552 554 556 |
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| index_date | 2024-07-03T17:24:46Z |
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| spelling | Landau, David P. 1941- Verfasser (DE-588)131584960 aut A guide to Monte Carlo simulations in statistical physics David P. Landau, Center for Simulational Physics, University of Georgia, USA, Kurt Binder, Institut für Physik, Johannes-Gutenberg-Universität, Germany Fifth edition Cambridge Cambridge University Press 2021 xvii, 564 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This fourth edition contains extensive new material describing numerous powerful algorithms not covered in previous editions, in some cases representing new developments that have only recently appeared. Older methodologies whose impact was previously unclear or unappreciated are also introduced, in addition to many small revisions that bring the text and cited literature up to date. This edition also introduces the use of petascale computing facilities in the Monte Carlo arena. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory Monte Carlo method Statistical physics Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 s Statistische Physik (DE-588)4057000-9 s DE-604 Binder, Kurt 1944-2022 Sonstige (DE-588)115452907 oth Erscheint auch als Online-Ausgabe 978-1-108-78034-6 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032709016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Landau, David P. 1941- A guide to Monte Carlo simulations in statistical physics Monte Carlo method Statistical physics Monte-Carlo-Simulation (DE-588)4240945-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4057000-9 |
| title | A guide to Monte Carlo simulations in statistical physics |
| title_auth | A guide to Monte Carlo simulations in statistical physics |
| title_exact_search | A guide to Monte Carlo simulations in statistical physics |
| title_exact_search_txtP | A guide to Monte Carlo simulations in statistical physics |
| title_full | A guide to Monte Carlo simulations in statistical physics David P. Landau, Center for Simulational Physics, University of Georgia, USA, Kurt Binder, Institut für Physik, Johannes-Gutenberg-Universität, Germany |
| title_fullStr | A guide to Monte Carlo simulations in statistical physics David P. Landau, Center for Simulational Physics, University of Georgia, USA, Kurt Binder, Institut für Physik, Johannes-Gutenberg-Universität, Germany |
| title_full_unstemmed | A guide to Monte Carlo simulations in statistical physics David P. Landau, Center for Simulational Physics, University of Georgia, USA, Kurt Binder, Institut für Physik, Johannes-Gutenberg-Universität, Germany |
| title_short | A guide to Monte Carlo simulations in statistical physics |
| title_sort | a guide to monte carlo simulations in statistical physics |
| topic | Monte Carlo method Statistical physics Monte-Carlo-Simulation (DE-588)4240945-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Monte Carlo method Statistical physics Monte-Carlo-Simulation Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032709016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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