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 2002
Ausgabe:	4., enl. ed.
Schriftenreihe:	Springer series in solid state sciences 80
Schlagwörter:	Monte Carlo method Random walks (Mathematics) Statistical physics Statistische Physik Monte-Carlo-Simulation
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009725276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XII, 180 S. Ill., graph. Darst.
ISBN:	3540432213

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Datensatz im Suchindex

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adam_text	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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3 RANDOM WALKS AND SELF-AV OIDING WALKS . . . . . . . . . . . . 8 2.1.4 THERMAL AVERAGES BY THE SIMPLE SAMPLING METHOD . . . 13 2.1.5 ADV ANTAGES 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.3 THE DYNAMIC INTERPRETATION OF THE IMPORTANCE SAMPLING MONTE CARLO METHOD . . . . . . . . . . . . . . . . . . . . . 29 2.2.4 STATISTICAL ERRORS AND TIME-DISPLACED RELAXATION FUNCTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 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 . . . . . . . 39 2.3.3 BROKEN SYMMETRY AND FINITE-SIZE EFFECTS AT THERMAL PHASE TRANSITIONS . . . . . . . . . . . . . . . . . . . . . . 42 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 BEHAV IOR OF RELAXATION TIMES . . . . . . . . . . . . 54 2.3.6 FINITE-SIZE SCALING WITHOUT HYPERSCALING . . . . . . . . . . 57 2.3.7 FINITE-SIZE SCALING FOR FIRST-ORDER PHASE TRANSITIONS . . . . . . . . . . . . . . . . . . . 58 XII CONTENTS 2.3.8 FINITE-SIZE BEHAVIOR OF STATISTICAL ERRORS AND THE PROBLEM OF SELF-AV ERAGING . . . . . . . . . . . . . . . . . . 65 2.4 REMARKS ON THE SCOPE OF THE THEORY CHAPTER . . . . . . . . . . . . . . 68 3. GUIDE TO PRACTICAL WORK WITH THE MONTE CARLO METHOD .. 69 3.1 AIMS OF THE GUIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2 SIMPLE SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2.1 RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.2.2 NONREV ERSAL RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . . 82 3.2.3 SELF-AV OIDING RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . 83 3.2.4 PERCOLATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3 BIASED SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.3.1 SELF-AV OIDING RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . 95 3.4 IMPORTANCE SAMPLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.4.1 ISING MODEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.4.2 SELF-AV OIDING RANDOM WALK . . . . . . . . . . . . . . . . . . . . . . . 112 4. SOME IMPORTANT RECENT DEVELOPMENTS OF THE MONTE CARLO METHODOLOGY ......................... 115 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.2 APPLICATION OF THE SWENDSEN*WANG CLUSTER ALGORITHM TO THE ISING MODEL . . . . . . . . . . . . . . . . . . . . . 117 4.3 REWEIGHTING METHODS IN THE STUDY OF PHASE DIAGRAMS, FIRST-ORDER PHASE TRANSITIONS, AND INTERFACIAL TENSIONS . . . . . . 122 4.4 SOME COMMENTS ON ADVANCES WITH FINITE-SIZE SCALING ANALYSES . . . . . . . . . . . . . . . . . . . . . . . . . 127 5. QUANTUM MONTE CARLO SIMULATIONS: AN INTRODUCTION ..... 137 5.1 QUANTUM STATISTICAL MECHANICS V S. CLASSICAL STATISTICAL MECHANICS . . . . . . . . . . . . . . . . . . . . . . . . 137 5.2 THE PATH INTEGRAL QUANTUM MONTE CARLO METHOD (PIMC) . . . 143 5.3 QUANTUM MONTE CARLO FOR LATTICE MODELS . . . . . . . . . . . . . . . . . 150 5.4 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 APPENDIX ..................................................... 159 A.1 ALGORITHM FOR THE RANDOM WALK PROBLEM . . . . . . . . . . . . . . . . . 159 A.2 ALGORITHM FOR CLUSTER IDENTIFICATION . . . . . . . . . . . . . . . . . . . . . . . 160 REFERENCES .................................................... 165 BIBLIOGRAPHY .................................................. 175 SUBJECT INDEX ................................................ 177
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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 Springer series in solid state sciences Monte Carlo method Random walks (Mathematics) Statistical physics Statistische Physik (DE-588)4057000-9 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd
subject_GND	(DE-588)4057000-9 (DE-588)4240945-7
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 K. Binder ; D. W. Heermann
title_fullStr	Monte Carlo simulation in statistical physics an introduction K. Binder ; D. W. Heermann
title_full_unstemmed	Monte Carlo simulation in statistical physics an introduction K. Binder ; D. 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 method Random walks (Mathematics) Statistical physics Statistische Physik (DE-588)4057000-9 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd
topic_facet	Monte Carlo method Random walks (Mathematics) Statistical physics Statistische Physik Monte-Carlo-Simulation
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009725276&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
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work_keys_str_mv	AT binderkurt montecarlosimulationinstatisticalphysicsanintroduction AT heermanndieterw montecarlosimulationinstatisticalphysicsanintroduction

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