Vertex models on random graphs:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
2002
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Leipzig, Univ., Diss., 2002 |
| Beschreibung: | XIII, 290, 8 S. Ill., graph. Darst. : 30 cm |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text |
CONTENTS
1 INTRODUCTION 1
2 THE DTRS APPROACH TO QUANTUM GRAVITY 7
2.1 PATH INTEGRALS AND GEOMETRIC THEORIES. 7
2.1.1 PATH INTEGRALS AND QUANTUM PATHS. 7
2.1.2 RANDOM SURFACES AND STRINGS. 9
2.1.3 QUANTUM GRAVITY. 10
2.1.4 THE CASE OF TWO DIMENSIONS . 13
2.2 SIMPLICIAL QUANTUM GRAVITY. 14
2.2.1 RANDOM WALKS AND THE WIENER MEASURE .14
2.2.2 DISCRETISING QUANTUM GRAVITY . 16
2.2.3 DYNAMICAL TRIANGULATIONS AND THE DISCRETISED ACTION. 19
2.3 ANALYTICAL RESULTS FOR THE DISCRETISED THEORY .24
2.3.1 EXISTENCE OF THE DISCRETISED PARTITION FUNCTION.25
2.3.2 STRING SUSCEPTIBILITY, MASS GAP AND STRING TENSION.27
2.3.3 THE COMBINATORIAL SOLUTION.30
2.3.4 MATRIX MODELS.33
2.3.5 FRACTAL STRUCTURE OF THE LATTICES.36
2.3.6 FURTHER RESULTS AND THE TRANSFER MATRIX.40
II
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/965641988
CONTENTS III
2.3.7 THE CONTINUUM LIMIT.42
2.4 DRESSING DYNAMICAL TRIANGULATIONS.44
2.4.1 ANNEALED AND QUENCHED DISORDER.44
2.4.2 THE KPZ/DDK SOLUTION.46
2.4.3 MATRIX MODEL EXAMPLES.49
3 THE SIMULATION OF DYNAMICAL GRAPHS 51
3.1 GRAPH ENSEMBLES.52
3.1.1 TRIANGULATIONS AND
4 Z GRAPHS.52
3.1.2 QUADRANGULATIONS AND /
4 GRAPHS.55
3.2 SIMULATION OF DYNAMICAL POLYGONIFICATIONS.57
3.2.1 MOVES AND ERGODICITY.58
3.2.2 DETAILED BALANCE AND PSEUDO GRAND-CANONICAL SIMULATIONS . 62
3.2.3 GENERALIZATION TO QUADRANGULATIONS.64
3.2.4 NECESSARY CHECKS AND IMPLEMENTATION DETAILS.68
3.3 THE CO-ORDINATION NUMBER DISTRIBUTION.74
3.3.1 COUNTING PLANAR GRAPHS .75
3.3.2 COMPARISON TO SIMULATION RESULTS.'. . 83
3.4 THE TWO-LINK FLIP FOR
(J A GRAPHS.91
3.5 ENHANCING THE EFFICIENCY.96
3.5.1 AUTOCORRELATION TIMES .96
3.5.2 THE BABY-UNIVERSE SURGERY METHOD.103
4 VERTEX MODELS AND THEIR SIMULATION 112
4.1 SQUARE-LATTICE VERTEX MODELS.113
4.1.1 DEFINITION AND BASIC PROPERTIES.113
IV
CONTENTS
4.1.2 EXACT SOLUTION OF THE ZERO-FIELD CASES .116
4.1.3 TRANSFORMATIONS AND SPECIALIZATIONS.121
4.2 THE LOOP ALGORITHM.124
4.2.1 IDEA AND OUTLINE. 125
4.2.2 CHOICE OF THE BREAKUP PROBABILITIES.128
4.2.3 PRACTICAL APPLICATION AND TESTS.131
4.3 VERTEX MODELS ON RANDOM
F 4 GRAPHS.135
4.3.1 ADDITIONAL SYMMETRY.135
4.3.2 THE ORDER PARAMETER. 137
4.3.3 IMPLEMENTATION OF THE SIMULATION SCHEME.142
5 THE 6-VERTEX MODEL ON RANDOM
(J)A
GRAPHS 147
5.1 ANALYTICAL RESULTS.148
5.1.1 THE CASE OF REGULAR LATTICES.148
5.1.2 VERTEX MODELS COUPLED TO QUANTUM GRAVITY.151
5.2 THE ANTI-FERROELECTRIC PHASE TRANSITION.156
5.2.1 SCALING AT AN INFINITE ORDER PHASE TRANSITION .157
5.2.2 THE SQUARE-LATTICE
F MODEL .159
5.2.3 THE
F MODEL ON PLANAR F 4 RANDOM GRAPHS.172
5.3 DYNAMICAL SCALING AND AUTOCORRELATION TIMES.,.199
5.3.1 LOCAL UPDATE .200
5.3.2 SURGERY UPDATE.206
5.4 GEOMETRICAL PROPERTIES.210
5.4.1 THE CO-ORDINATION NUMBER DISTRIBUTION.211
5.4.2 THE STRING SUSCEPTIBILITY EXPONENT.216
5.4.3 THE HAUSDORFF DIMENSION.226
CONTENTS
V
6 CONCLUSIONS AND OUTLOOK 240
A METHODS OF SIMULATION AND DATA ANALYSIS 246
A.L THE MONTE CARLO PROCESS.246
A. 1.1 SIMPLE SAMPLING.246
A. 1.2 IMPORTANCE SAMPLING.247
A.2 AUTOCORRELATIONS AND DYNAMICAL SCALING.249
A.3 BINNING AND THE JACKKNIFE.252
A.3.1 THE BINNING TECHNIQUE.* 252
A.3.2 JACKKNIFE BIAS AND VARIANCE ESTIMATES.253
A.4 ESTIMATION OF AUTOCORRELATION TIMES.257
A.5 HISTOGRAM REWEIGHTING.260
B GRAPH EMBEDDING AND VISUALIZATION 263
BIBLIOGRAPHY 266
ACKNOWLEDGEMENTS 289
CURRICULUM VITAE
290 |
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| id | DE-604.BV015823199 |
| illustrated | Illustrated |
| indexdate | 2024-11-22T17:35:23Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010130163 |
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| physical | XIII, 290, 8 S. Ill., graph. Darst. : 30 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| record_format | marc |
| spelling | Weigel, Martin 1972- Verfasser (DE-588)12421892X aut Vertex models on random graphs vorgelegt von Martin Weigel 2002 XIII, 290, 8 S. Ill., graph. Darst. : 30 cm txt rdacontent n rdamedia nc rdacarrier Leipzig, Univ., Diss., 2002 Vertex-Modell (DE-588)4337907-2 gnd rswk-swf Quantengravitation (DE-588)4124012-1 gnd rswk-swf Zufallsgraph (DE-588)4277661-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Quantengravitation (DE-588)4124012-1 s Vertex-Modell (DE-588)4337907-2 s Zufallsgraph (DE-588)4277661-2 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010130163&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Weigel, Martin 1972- Vertex models on random graphs Vertex-Modell (DE-588)4337907-2 gnd Quantengravitation (DE-588)4124012-1 gnd Zufallsgraph (DE-588)4277661-2 gnd |
| subject_GND | (DE-588)4337907-2 (DE-588)4124012-1 (DE-588)4277661-2 (DE-588)4113937-9 |
| title | Vertex models on random graphs |
| title_auth | Vertex models on random graphs |
| title_exact_search | Vertex models on random graphs |
| title_full | Vertex models on random graphs vorgelegt von Martin Weigel |
| title_fullStr | Vertex models on random graphs vorgelegt von Martin Weigel |
| title_full_unstemmed | Vertex models on random graphs vorgelegt von Martin Weigel |
| title_short | Vertex models on random graphs |
| title_sort | vertex models on random graphs |
| topic | Vertex-Modell (DE-588)4337907-2 gnd Quantengravitation (DE-588)4124012-1 gnd Zufallsgraph (DE-588)4277661-2 gnd |
| topic_facet | Vertex-Modell Quantengravitation Zufallsgraph Hochschulschrift |
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