Verfügbarkeit: Monte Carlo simulation in statistical physics

Monte Carlo simulation in statistical physics: an introduction

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Bibliographische Detailangaben
Beteiligte Personen:	Binder, Kurt 1944-2022 (VerfasserIn), Heermann, Dieter W. 1955- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin [u.a.] Springer 2010
Ausgabe:	5. ed.
Schriftenreihe:	Graduate Texts in Physics
Schlagwörter:	Monte-Carlo-Simulation Statistische Physik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020575304&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XIV, 200 S. Ill., graph. Darst.
ISBN:	9783642031625 9783642031632

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MARC


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Datensatz im Suchindex

DE-BY-TUM_call_number	0202 PHY 016f 2011 A 4918(5)
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adam_text	IMAGE 1 CONTENTS 1 INTRODUCTION: PURPOSE AND SCOPE OF THIS VOLUME, AND SOME GENERAL COMMENTS . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 1 2 THEORETICAL FOUNDATIONS OF THE MONTE CARLO METHOD AND ITS APPLICATIONS IN STATISTICAL PHYSICS .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 5 2.1 SIMPLE SAMPLING VERSUS IMPORTANCE SAMPLING .. . . . . . . . . . . . . . . . .. . . . . . . 5 2.1.1 MODELS .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 5 2.1.2 SIMPLE SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 7 2.1.3 RANDOM WALKS AND SELF-AVOIDING WALKS . . . . . . . . . . . . . . . .. . . . . . . 8 2.1.4 THERMAL AVERAGES BY THE SIMPLE SAMPLING METHOD . . . .. . . . . . . 13 2.1.5 ADVANTAGES AND LIMITATIONS OF SIMPLE SAMPLING . . . . . . .. . . . . . . 14 2.1.6 IMPORTANCE SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 17 2.1.7 MORE ABOUT MODELS AND ALGORITHMS .. . . . . . . . . . . . . . . . . . . .. . . . . . . 20 2.2 ORGANIZATION OF MONTE CARLO PROGRAMS, AND THE DYNAMIC INTERPRETATION OF MONTE CARLO SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 23 2.2.1 FIRST COMMENTS ON THE SIMULATION OF THE ISING MODEL ... . . . . . . 23 2.2.2 BOUNDARY CONDITIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 25 2.2.3 THE DYNAMIC INTERPRETATION OF THE IMPORTANCE SAMPLING MONTE CARLO METHOD . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 28 2.2.4 STATISTICAL ERRORS AND TIME-DISPLACED RELAXATION FUNCTIONS . . 32 2.3 FINITE-SIZE EFFECTS .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 35 2.3.1 FINITE-SIZE EFFECTS AT THE PERCOLATION TRANSITION .. . . . . . . .. . . . . . . 35 2.3.2 FINITE-SIZE SCALING FOR THE PERCOLATION PROBLEM .. . . . . . . .. . . . . . . 38 2.3.3 BROKEN SYMMETRY AND FINITE-SIZE EFFECTS AT THERMAL PHASE TRANSITIONS .. . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 41 2.3.4 THE ORDER PARAMETER PROBABILITY DISTRIBUTION AND ITS USE TO JUSTIFY FINITE-SIZE SCALING AND PHENOMENOLOGICAL RENORMALIZATION .. . . . . . . . . . . . . . . .. . . . . . . 44 2.3.5 FINITE-SIZE BEHAVIOR OF RELAXATION TIMES . . . . . . . . . . . . . . .. . . . . . . 52 2.3.6 FINITE-SIZE SCALING WITHOUT HYPERSCALING . . . . . . . . . . . .. . . . . . . 56 2.3.7 FINITE-SIZE SCALING FOR FIRST-ORDER PHASE TRANSITIONS .. .. . . . . . . 56 2.3.8 FINITE-SIZE BEHAVIOR OF STATISTICAL ERRORS AND THE PROBLEM OF SELF-AVERAGING.. . . . . . . . . . . . . . . . . . . . . .. . . . . . . 62 2.4 REMARKS ON THE SCOPE OF THE THEORY CHAPTER . . . . . . . . . . . . . . . . . . .. . . . . . . 67 XIII IMAGE 2 XIV CONTENTS 3 GUIDE TO PRACTICAL WORK WITH THE MONTE CARLO METHOD . . . . . . . . . . .. . . . . . . 69 3.1 AIMS OF THE GUIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 71 3.2 SIMPLE SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 74 3.2.1 RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 74 3.2.2 NONREVERSAL RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 81 3.2.3 SELF-AVOIDING RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 82 3.2.4 PERCOLATION .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 86 3.3 BIASED SAMPLING .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 93 3.3.1 SELF-AVOIDING RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 94 3.4 IMPORTANCE SAMPLING .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 96 3.4.1 ISING MODEL .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 96 3.4.2 SELF-AVOIDING RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 110 4 SOME IMPORTANT RECENT DEVELOPMENTS OF THE MONTE CARLO METHODOLOGY .. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .111 4.1 INTRODUCTION .. . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 111 4.2 APPLICATION OF THE SWENDSEN-WANG CLUSTER ALGORITHM TO THE ISING MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 113 4.3 REWEIGHTING METHODS IN THE STUDY OF PHASE DIAGRAMS, FIRST-ORDER PHASE TRANSITIONS, AND INTERFACIAL TENSIONS . . . . . . . . .. . . . . . . 118 4.4 SOME COMMENTS ON ADVANCES WITH FINITE-SIZE SCALING ANALYSES . . . . 123 5 QUANTUM MONTE CARLO SIMULATIONS: AN INTRODUCTION .. . . . . . . . . . . . .. . . . . . .131 5.1 QUANTUM STATISTICAL MECHANICS VERSUS CLASSICAL STATISTICAL MECHANICS .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 131 5.2 THE PATH INTEGRAL QUANTUM MONTE CARLO METHOD . . . . . . . . . . . . . . .. . . . . . . 137 5.3 QUANTUM MONTE CARLO FOR LATTICE MODELS . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 143 5.4 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 152 6 MONTE CARLO METHODS FOR THE SAMPLING OF FREE ENERGY LANDSCAPES . . . .153 6.1 INTRODUCTION AND OVERVIEW .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 153 6.2 UMBRELLA SAMPLING .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 161 6.3 MULTICANONICAL SAMPLING AND OTHER EXTENDED ENSEMBLE METHODS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 164 6.4 WANG-LANDAU SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 166 6.5 TRANSITION PATH SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 169 6.6 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 173 APPENDIX . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .175 A.1 ALGORITHM FOR THE RANDOM WALK PROBLEM . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 175 A.2 ALGORITHM FOR CLUSTER IDENTIFICATION .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . 176 REFERENCES .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .181 BIBLIOGRAPHY . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .193 SUBJECT INDEX . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .197
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author	Binder, Kurt 1944-2022 Heermann, Dieter W. 1955-
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spellingShingle	Binder, Kurt 1944-2022 Heermann, Dieter W. 1955- Monte Carlo simulation in statistical physics an introduction 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	Monte Carlo simulation in statistical physics an introduction
title_auth	Monte Carlo simulation in statistical physics an introduction
title_exact_search	Monte Carlo simulation in statistical physics an introduction
title_full	Monte Carlo simulation in statistical physics an introduction Kurt Binder ; Dieter W. Heermann
title_fullStr	Monte Carlo simulation in statistical physics an introduction Kurt Binder ; Dieter W. Heermann
title_full_unstemmed	Monte Carlo simulation in statistical physics an introduction Kurt Binder ; Dieter W. Heermann
title_short	Monte Carlo simulation in statistical physics
title_sort	monte carlo simulation in statistical physics an introduction
title_sub	an introduction
topic	Monte-Carlo-Simulation (DE-588)4240945-7 gnd Statistische Physik (DE-588)4057000-9 gnd
topic_facet	Monte-Carlo-Simulation Statistische Physik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020575304&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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