Holdings: A guide to Monte Carlo simulations in statistical physics

A guide to Monte Carlo simulations in statistical physics:

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Bibliographic Details
Main Author:	Landau, David P. 1941- (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2002
Edition:	[Nachdr.]
Subjects:	Monte-Carlo-Simulation Statistische Physik
Online Access:	Sample text Publisher description Table of contents Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	XIII, 384 S. graph. Darst.
ISBN:	0521653142 0521653665

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MARC


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Record in the Search Index

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adam_text	AGUIDE TO MONTE CARLO SIMULATIONS IN STATISTICAL PHYSICS DAVID P. LANDAU CENTER FOR SIMULATIONAL PHYSICS, THE UNIVERSITY OF GEORGIA KURT BINDER INSTITUT FUER PHYSIK, JOHANNES-GUTENBERG-UNIVERSITAET MAINZ CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE XI 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 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 MARKOV CHAINS 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 46 3 SIMPLE SAMPLING MONTE CARLO METHODS 48 3.1 INTRODUCTION 48 3.2 COMPARISONS OF METHODS FOR NUMERICAL INTEGRATION OF GIVEN FUNCTIONS 48 VI CONTENTS 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 MODEIS 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 MODEIS 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 MODEIS 105 4.3.1 ISING MODEIS WITH COMPETING INTERACTIONS 105 4.3.2 ^-STATE POTTS MODEIS 109 4.3.3 BAXTER AND BAXTER-WU MODEIS 110 4.3.4 CLOCK MODEIS 112 4.3.5 ISING SPIN GLASS MODEIS 112 4.3.6 COMPLEX FLUID MODEIS 113 4.4 SPIN-EXCHANGE SAMPLING 114 4.4.1 CONSTANT MAGNETIZATION SIMULATIONS 114 4.4.2 PHASE SEPARATION 115 4.4.3 DIFFUSION 117 4.4.4 HYDRODYNAMIC SLOWING DOWN 119 4.5 MICROCANONICAL METHODS 119 4.5.1 DEMON ALGORITHM 119 4.5.2 DYNAMIC ENSEMBLE 120 4.5.3 Q2R 120 4.6 GENERAL REMARKS, CHOICE OF ENSEMBLE 121 CONTENTS VII 4.7 STATICS AND DYNAMICS OF POLYMER MODEIS ON LATTICES 121 4.7.1 BACKGROUND 121 4.7.2 FIXED LENGTH BOND METHODS 122 4.7.3 BOND FLUCTUATION METHOD 123 4.7.4 POLYMERS IN SOLUTIONS OF VARIABLE QUALITY: OE-POINT, COLLAPSE TRANSITION, UNMIXING 124 4.7.5 EQUILIBRIUM POLYMERS: A CASE STUDY 127 4.8 SOME ADVICE 130 REFERENCES 130 5 MORE ON IMPORTANCE SAMPLING MONTE CARLO METHODS FOR LATTICE SYSTEMS 133 5.1 CLUSTER FLIPPING METHODS 133 5.1.1 FORTUIN-KASTELEYN THEOREM 133 5.1.2 SWENDSEN*WANG METHOD 134 5.1.3 WOLFF METHOD 137 5.1.4 IMPROVED ESTIMATORS 138 5.2 SPECIALIZED COMPUTATIONAL TECHNIQUES 139 5.2.1 EXPANDED ENSEMBLE METHODS 139 5.2.2 MULTISPIN CODING 139 5.2.3 IV-FOLD WAY AND EXTENSIONS 140 5.2.4 HYBRID ALGORITHMS 142 5.2.5 MULTIGRID ALGORITHMS 142 5.2.6 MONTE CARLO ON VECTOR COMPUTERS 143 5.2.7 MONTE CARLO ON PARALLEL COMPUTERS 143 5.3 CLASSICAL SPIN MODEIS 144 5.3.1 INTRODUCTION 144 5.3.2 SIMPLE SPIN-FLIP METHOD 144 5.3.3 HEATBATH METHOD 146 5.3.4 LOW TEMPERATURE TECHNIQUES 147 5.3.5 OVER-RELAXATION METHODS 147 5.3.6 WOLFF EMBEDDING TRICK AND CLUSTER FLIPPING 148 5.3.7 HYBRID METHODS 149 5.3.8 MONTE CARLO DYNAMICS VS. EQUATION OF MOTION DYNAMICS 150 5.3.9 TOPOLOGICAL EXCITATIONS AND SOLITONS 150 5.4 SYSTEMS WITH QUENCHED RANDOMNESS 154 5.4.1 GENERAL COMMENTS: AVERAGING IN RANDOM SYSTEMS 154 5.4.2 RANDOM FIELDS AND RANDOM BONDS 157 5.4.3 SPIN GLASSES AND OPTIMIZATION BY SIMULATED ANNEALING 158 5.5 MODELS WITH MIXED DEGREES OF FREEDOM: SI/GE ALLOYS, A CASE STUDY 163 5.6 SAMPLING THE FREE ENERGY AND ENTROPY 164 5.6.1 THERMODYNAMIC INTEGRATION 164 5.6.2 GROUNDSTATE FREE ENERGY DETERMINATION 166 5.6.3 ESTIMATION OF INTENSIVE VARIABLES: THE CHEMICAL POTENTIAL 166 5.6.4 LEE-KOSTERLITZ METHOD 167 VIII CONTENTS 5.6.5 FREE ENERGY FROM FINITE SIZE DEPENDENCE AT T C 167 5.7 MISCELLANEOUS TOPICS 168 5.7.1 INHOMOGENEOUS SYSTEMS: SURFACES, INTERFACES, ETC. 168 5.7.2 OTHER MONTE CARLO SCHEMES 173 5.7.3 FINITE SIZE EFFECTS: A REVIEW AND SUMMARY 174 5.7.4 MORE ABOUT ERROR ESTIMATION 175 5.7.5 RANDOM NUMBER GENERATORS REVISITED 176 5.8 SUMMARY AND PERSPECTIVE 178 REFERENCES 179 6 OFF-LATTICE MODEIS 182 6.1 FLUIDS 182 6.1.1 NVT ENSEMBLE AND THE VIRIAL THEOREM 182 6.1.2 NPT ENSEMBLE 185 6.1.3 GRAND CANONICAL ENSEMBLE 189 6.1.4 SUBSYSTEMS: A CASE STUDY 192 6.1.5 GIBBS ENSEMBLE 197 6.1.6 WIDOM PARTICLE INSERTION METHOD AND VARIANTS 200 6.2 SHORT RAENGE INTERACTIONS 202 6.2.1 CUTOFFS 202 6.2.2 VERLET TABLES AND CELL STRUCTURE 202 6.2.3 MINIMUM IMAGE CONVENTION 202 6.2.4 MIXED DEGREES OF FREEDOM RECONSIDERED 203 6.3 TREATMENT OF LONG RAENGE FORCES 203 6.3.1 REACTION FIELD METHOD 203 6.3.2 EWALD METHOD 204 6.3.3 FAST MULTIPOLE METHOD 204 6.4 ADSORBED MONOLAYERS 205 6.4.1 SMOOTH SUBSTRATES 205 6.4.2 PERIODIC SUBSTRATE POTENTIALS 206 6.5 COMPLEX FLUIDS 207 6.6 POLYMERS: AN INTRODUCTION 210 6.6.1 LENGTH SCALES AND MODEIS 210 6.6.2 ASYMMETRIE POLYMER MIXTURES: A CASE STUDY 216 6.6.3 APPLICATIONS: DYNAMICS OF POLYMER MELTS; THIN ADSORBED POLYMERIE FILMS 219 6.7 CONFIGURATIONAL BIAS AND SMART MONTE CARLO 224 REFERENCES 227 7 REWEIGHTING METHODS 230 7.1 BACKGROUND 230 7.1.1 DISTRIBUTION FUNETIONS 230 7.1.2 UMBRELLA SAMPLING 230 7.2 SINGLE HISTOGRAM METHOD: THE ISING MODEL AS A CASE STUDY 233 7.3 MULTI-HISTOGRAM METHOD 240 7.4 BROAD HISTOGRAM METHOD 240 7.5 MULTICANONICAL SAMPLING 241 CONTENTS IX 7.5.1 THE MULTICANONICAL APPROACH AND ITS RELATIONSHIP TO CANONICAL SAMPLING 241 7.5.2 NEAR FIRST ORDER TRANSITIONS 243 7.5.3 GROUNDSTATES IN COMPLICATED ENERGY LANDSCAPES 244 7.5.4 INTERFACE FREE ENERGY ESTIMATION 245 7.6 A CASE STUDY: THE CASIMIR EFFECT IN CRITICAL SYSTEMS 246 REFERENCES 248 8 QUANTUM MONTE CARLO METHODS 250 8.1 INTRODUCTION 250 8.2 FEYNMAN PATH INTEGRAL FORMULATION 252 8.2.1 OFF-LATTICE PROBLEMS: LOW-TEMPERATURE PROPERTIES OF CRYSTALS 252 8.2.2 BOESE STATISTICS AND SUPERFLUIDITY 258 8.2.3 PATH INTEGRAL FORMULATION FOR ROTATIONAL DEGREES OF FREEDOM 259 8.3 LATTICE PROBLEMS 261 8.3.1 THE ISING MODEL IN A TRANSVERSE FIELD 261 8.3.2 ANISOTROPIE HEISENBERG CHAIN 263 8.3.3 FERMIONS ON A LATTICE 266 8.3.4 AN INTERMEZZO: THE MINUS SIGN PROBLEM 269 8.3.5 SPINLESS FERMIONS REVISITED 271 8.3.6 CLUSTER METHODS FOR QUANTUM LATTICE MODEIS 274 8.3.7 DECOUPLED CELL METHOD 275 8.3.8 HANDSCOMB S METHOD 276 8.3.9 FERMION DETERMINANTS 277 8.4 MONTE CARLO METHODS FOR THE STUDY OF GROUNDSTATE PROPERTIES 278 8.4.1 VARIATIONAL MONTE CARLO (VMC) 279 8.4.2 GREEN S FUNETION MONTE CARLO METHODS (GFMC) 280 8.5 CONCLUDING REMARKS 283 REFERENCES 283 9 MONTE CARLO RENORMALIZATION GROUP METHODS 286 9.1 INTRODUCTION TO RENORMALIZATION GROUP THEORY 286 9.2 REAL SPACE RENORMALIZATION GROUP 290 9.3 MONTE CARLO RENORMALIZATION GROUP 291 9.3.1 LARGE CELL RENORMALIZATION 291 9.3.2 MA S METHOD: FINDING CRITICAL EXPONENTS AND THE FIXED POINT HAMILTONIAN 293 9.3.3 SWENDSEN S METHOD 294 9.3.4 LOCATION OF PHASE BOUNDARIES 296 9.3.5 DYNAMIC PROBLEMS: MATCHING TIME-DEPENDENT CORRELATION FUNETIONS 297 REFERENCES 298 10 NON-EQUILIBRIUM AND IRREVERSIBLE PROCESSES 299 10.1 INTRODUCTION AND PERSPECTIVE 299 10.2 DRIVEN DIFFUSIVE SYSTEMS (DRIVEN LATTICE GASES) 299 10.3 CRYSTAL GROWTH 301 X CONTENTS 10.4 DOMAIN GROWTH 304 10.5 POLYMER GROWTH 306 10.5.1 LINEAR POLYMERS 306 10.5.2 GELATION 306 10.6 GROWTH OF STRUCTURES AND PATTERNS 308 10.6.1 EDEN MODEL OF CLUSTER GROWTH 308 10.6.2 DIFFUSION LIMITED AGGREGATION 308 10.6.3 CLUSTER-CLUSTER AGGREGATION 311 10.6.4 CELLULAR AUTOMATA 311 10.7 MODELS FOR FILM GROWTH 312 10.7.1 BACKGROUND 312 10.7.2 BALLISTIC DEPOSITION 313 10.7.3 SEDIMENTATION 314 10.7.4 KINETIC MONTE CARLO AND MBE GROWTH 315 10.8 OUTLOOK: VARIATIONS ON A THEME 317 REFERENCES 318 11 LATTICE GAUGE MODEIS: A BRIEF INTRODUCTION 320 11.1 INTRODUCTION: GAUGE INVARIANCE AND LATTICE GAUGE THEORY 320 11.2 SOME TECHNICAL MATTERS 322 11.3 RESULTS FOR Z{N) LATTICE GAUGE MODEIS 322 11.4 COMPACT U(L) GAUGE THEORY 323 11.5 SU(2) LATTICE GAUGE THEORY 324 11.6 INTRODUCTION: QUANTUM CHROMODYNAMICS (QCD) AND PHASE TRANSITIONS OF NUCLEAR MATTER 325 11.7 THE DECONFINEMENT TRANSITION OF QCD 327 REFERENCES 330 12 A BRIEF REVIEW OF OTHER METHODS OF COMPUTER SIMULATION 332 12.1 INTRODUCTION 332 12.2 MOLECULAR DYNAMICS 332 12.2.1 INTEGRATION METHODS (MICROCANONICAL ENSEMBLE) 332 12.2.2 OTHER ENSEMBLES (CONSTANT TEMPERATURE, CONSTANT PRESSURE, ETC.) 336 12.2.3 NON-EQUILIBRIUM MOLECULAR DYNAMICS 339 12.2.4 HYBRID METHODS (MD + MC) 339 12.2.5 AB INITIO MOLECULAR DYNAMICS 339 12.3 QUASI-CLASSICAL SPIN DYNAMICS 340 12.4 LANGEVIN EQUATIONS AND VARIATIONS (CELL DYNAMICS) 343 12.5 LATTICE GAS CELLULAR AUTOMATA 344 REFERENCES 345 13 OUTLOOK 346 APPENDIX: LISTING OF PROGRAMS MENTIONED IN THE TEXT 348 INDEX 379
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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 ; Kurt Binder Monte Carlo simulations in statistical physics [Nachdr.] Cambridge [u.a.] Cambridge Univ. Press 2002 XIII, 384 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Monte-Carlo-Simulation swd Statistische Physik swd 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 Sonstige oth http://www.loc.gov/catdir/samples/cam034/99038308.html Sample text http://www.loc.gov/catdir/description/cam0210/99038308.html Publisher description http://www.loc.gov/catdir/toc/cam021/99038308.html Table of contents GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012785349&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-Simulation swd Statistische Physik swd 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_alt	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_full	A guide to Monte Carlo simulations in statistical physics David P. Landau ; Kurt Binder
title_fullStr	A guide to Monte Carlo simulations in statistical physics David P. Landau ; Kurt Binder
title_full_unstemmed	A guide to Monte Carlo simulations in statistical physics David P. Landau ; Kurt Binder
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-Simulation swd Statistische Physik swd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Statistische Physik (DE-588)4057000-9 gnd
topic_facet	Monte-Carlo-Simulation Statistische Physik
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