Monte Carlo simulation in statistical physics: an introduction
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2010
|
| Ausgabe: | 5. ed. |
| Schriftenreihe: | Graduate Texts in Physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 200 S. Ill., graph. Darst. |
| ISBN: | 9783642031625 9783642031632 |
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| 245 | 1 | 0 | |a Monte Carlo simulation in statistical physics |b an introduction |c Kurt Binder ; Dieter W. Heermann |
| 250 | |a 5. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
| 300 | |a XIV, 200 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
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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 |
| any_adam_object | 1 |
| author | Binder, Kurt 1944-2022 Heermann, Dieter W. 1955- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-raw | 530.1301518282 |
| dewey-search | 530.1301518282 |
| dewey-sort | 3530.1301518282 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| edition | 5. ed. |
| format | Book |
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| id | DE-604.BV036655888 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T04:20:29Z |
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| isbn | 9783642031625 9783642031632 |
| language | English |
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| physical | XIV, 200 S. Ill., graph. Darst. |
| publishDate | 2010 |
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| publisher | Springer |
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| spelling | Binder, Kurt 1944-2022 Verfasser (DE-588)115452907 aut Monte Carlo simulation in statistical physics an introduction Kurt Binder ; Dieter W. Heermann 5. ed. Berlin [u.a.] Springer 2010 XIV, 200 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate Texts in Physics Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Statistische Physik (DE-588)4057000-9 s Monte-Carlo-Simulation (DE-588)4240945-7 s DE-604 Heermann, Dieter W. 1955- Verfasser (DE-588)115452974 aut SWB Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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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