Gibbs measures and phase transitions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
2011
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | De Gruyter studies in mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [495] - 537 |
| Beschreibung: | XIV, 545 S. |
| ISBN: | 9783110250299 |
Internformat
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| 100 | 1 | |a Georgii, Hans-Otto |d 1944-2017 |e Verfasser |0 (DE-588)10807546X |4 aut | |
| 245 | 1 | 0 | |a Gibbs measures and phase transitions |c Hans-Otto Georgii |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 2011 | |
| 300 | |a XIV, 545 S. | ||
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| 490 | 1 | |a De Gruyter studies in mathematics |v 9 | |
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Datensatz im Suchindex
| _version_ | 1804143859662323712 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
INTRODUCTION 1
PART I. GENERAL THEORY AND BASIC EXAMPLES 9
CHAPTER 1 SPECIFICATIONS OF RANDOM FIELDS 11
1.1 PRELIMINARIES 11
1.2 PRESCRIBING CONDITIONAL PROBABILITIES 15
1.3 -SPECIFICATIONS 18
CHAPTER 2 GIBBSIAN SPECIFICATIONS 25
2.1 POTENTIALS 26
2.2 QUASILOCALITY 30
2.3 GIBBS REPRESENTATION OF PRE-MODIFICATIONS 35
2.4 EQUIVALENCE OF POTENTIALS 39
CHAPTER 3 FINITE STATE MARKOV CHAINS AS GIBBS MEASURES 44
3.1 MARKOV SPECIFICATIONS ON THE INTEGERS 44
3.2 THE ONE-DIMENSIONAL ISING MODEL 49
3.A APPENDIX. POSITIVE MATRICES 54
CHAPTER 4 THE EXISTENCE PROBLEM 57
4.1 LOCAL CONVERGENCE OF RANDOM FIELDS 58
4.2 EXISTENCE OF CLUSTER POINTS 60
4.3 CONTINUITY RESULTS 66
4.4 EXISTENCE AND TOPOLOGICAL PROPERTIES OF GIBBS MEASURES 71 4.A
APPENDIX. STANDARD BOREL SPACES 73
CHAPTER 5 SPECIFICATIONS WITH SYMMETRIES 81
5.1 TRANSFORMATIONS OF SPECIFICATIONS 81
5.2 GIBBS MEASURES WITH SYMMETRIES 85
CHAPTER 6 THREE EXAMPLES OF SYMMETRY BREAKING 94
6.1 INHOMOGENEOUS ISING CHAINS 95
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010341634
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
6.2 THE ISING FERROMAGNET IN TWO DIMENSIONS 99
6.3 SHLOSMAN S RANDOM STAIRCASES 106
CHAPTER 7 EXTREME GIBBS MEASURES 114
7.1 TAIL TRIVIALITY AND APPROXIMATION 115
7.2 SOME APPLICATIONS 125
7.3 EXTREME DECOMPOSITION 129
7.4 MACROSCOPIC EQUIVALENCE OF GIBBS SIMPLICES 136
CHAPTER 8 UNIQUENESS 140
8.1 DOBRUSHIN S CONDITION OF WEAK DEPENDENCE 140
8.2 FURTHER CONSEQUENCES OF DOBRUSHIN S CONDITION 153
8.3 UNIQUENESS IN ONE DIMENSION 164
CHAPTER 9 ABSENCE OF SYMMETRY BREAKING. NON-EXISTENCE 168
9.1 DISCRETE SYMMETRIES IN ONE DIMENSION 169
9.2 CONTINUOUS SYMMETRIES IN TWO DIMENSIONS 178
PART II. MARKOV CHAINS AND GAUSS FIELDS AS GIBBS MEASURES 189
CHAPTER 10 MARKOV FIELDS ON THE INTEGERS I 190
10.1 TWO-SIDED AND ONE-SIDED MARKOV PROPERTY 191
10.2 MARKOV FIELDS WHICH ARE MARKOV CHAINS 196
10.3 UNIQUENESS OF THE SHIFT-INVARIANT MARKOV FIELD 204
CHAPTER 11 MARKOV FIELDS ON THE INTEGERS II 209
11.1 BOUNDARY LAWS, UNIQUENESS, AND NON-EXISTENCE 210
11.2 THE SPITZER-COX EXAMPLE OF PHASE TRANSITION 221
11.3 KALIKOW S EXAMPLE OF PHASE TRANSITION 228
11.4 SPITZER S EXAMPLE OF TOTALLY BROKEN SHIFT-INVARIANCE 233
CHAPTER 12 MARKOV FIELDS ON TREES 238
12.1 MARKOV CHAINS AND BOUNDARY LAWS 238
12.2 THE ISING MODEL ON CAYLEY TREES 247
CHAPTER 13 GAUSSIAN FIELDS 256
13.1 GAUSS FIELDS AS GIBBS MEASURES 257
13.2 GIBBS MEASURES FOR GAUSSIAN SPECIFICATIONS 267
13.3 THE HOMOGENEOUS CASE 273
13. A APPENDIX. SOME TOOLS OF GAUSSIAN ANALYSIS 284
IMAGE 3
CONTENTS XIII
PART III. SHIFT-INVARIANT GIBBS MEASURES 289
CHAPTER 14 ERGODICITY 290
14.1 ERGODIC RANDOM FIELDS 290
14.2 ERGODIC GIBBS MEASURES 296
14.A APPENDIX. THE MULTIDIMENSIONAL ERGODIC THEOREM 302
CHAPTER 15 THE SPECIFIC FREE ENERGY AND ITS MINIMIZATION 308
15.1 RELATIVE ENTROPY 309
15.2 SPECIFIC ENTROPY 312
15.3 SPECIFIC ENERGY AND FREE ENERGY 319
15.4 THE VARIATIONAL PRINCIPLE 323
15.5 LARGE DEVIATIONS AND EQUIVALENCE OF ENSEMBLES 327
CHAPTER 16 CONVEX GEOMETRY AND THE PHASE DIAGRAM 338
16.1 THE PRESSURE AND ITS TANGENT FUNCTIONALS 338
16.2 A GEOMETRIC VIEW OF GIBBS MEASURES 343
16.3 PHASE TRANSITIONS WITH PRESCRIBED ORDER PARAMETERS 348 16.4
UBIQUITY OF PURE PHASES 359
PART IV. PHASE TRANSITIONS IN REFLECTION POSITIVE MODELS 365
CHAPTER 17 REFLECTION POSITIVITY 367
17.1 THE CHESSBOARD ESTIMATE 367
17.2 GIBBS DISTRIBUTIONS WITH PERIODIC BOUNDARY CONDITION 374
CHAPTER 18 LOW ENERGY OCEANS AND DISCRETE SYMMETRY BREAKING 382
18.1 PERCOLATION OF SPIN PATTERNS 383
18.2 DISCRETE SYMMETRY BREAKING AT LOW TEMPERATURES 394
18.3 EXAMPLES 398
CHAPTER 19 PHASE TRANSITIONS WITHOUT SYMMETRY BREAKING 408
19.1 POTENTIALS WITH DEGENERATED GROUND STATES, AND PERTURBATIONS
THEREOF 408
19.2 EXPLOITING SPERNER S LEMMA 415
19.3 MODELS WITH AN ENTROPY-ENERGY CONFLICT 420
19.A APPENDIX. SPERNER S LEMMA 431
CHAPTER 20 CONTINUOUS SYMMETRY BREAKING IN N-VECTOR MODELS 433
20.1 SOME PRELIMINARIES 434
20.2 SPIN WAVE ANALYSIS, AND SPONTANEOUS MAGNETIZATION 439
IMAGE 4
XIV CONTENTS
BIBLIOGRAPHICAL NOTES 453
FURTHER PROGRESS 489
REFERENCES 495
REFERENCES TO THE SECOND EDITION 532
LIST OF SYMBOLS 539
INDEX 541
|
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| author | Georgii, Hans-Otto 1944-2017 |
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| author_sort | Georgii, Hans-Otto 1944-2017 |
| author_variant | h o g hog |
| building | Verbundindex |
| bvnumber | BV037246726 |
| classification_rvk | SK 800 SK 820 UG 3100 |
| classification_tum | MAT 605f MAT 285f PHY 065f |
| ctrlnum | (OCoLC)711832844 (DE-599)BVBBV037246726 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:54:22Z |
| institution | BVB |
| isbn | 9783110250299 |
| language | English |
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| physical | XIV, 545 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
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| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Georgii, Hans-Otto 1944-2017 Verfasser (DE-588)10807546X aut Gibbs measures and phase transitions Hans-Otto Georgii 2. ed. Berlin [u.a.] de Gruyter 2011 XIV, 545 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 9 Literaturverz. S. [495] - 537 Gibbs-Maß (DE-588)4157328-6 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s Gibbs-Maß (DE-588)4157328-6 s DE-604 De Gruyter studies in mathematics 9 (DE-604)BV000005407 9 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021160116&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Georgii, Hans-Otto 1944-2017 Gibbs measures and phase transitions De Gruyter studies in mathematics Gibbs-Maß (DE-588)4157328-6 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| subject_GND | (DE-588)4157328-6 (DE-588)4132140-6 |
| title | Gibbs measures and phase transitions |
| title_auth | Gibbs measures and phase transitions |
| title_exact_search | Gibbs measures and phase transitions |
| title_full | Gibbs measures and phase transitions Hans-Otto Georgii |
| title_fullStr | Gibbs measures and phase transitions Hans-Otto Georgii |
| title_full_unstemmed | Gibbs measures and phase transitions Hans-Otto Georgii |
| title_short | Gibbs measures and phase transitions |
| title_sort | gibbs measures and phase transitions |
| topic | Gibbs-Maß (DE-588)4157328-6 gnd Phasenumwandlung (DE-588)4132140-6 gnd |
| topic_facet | Gibbs-Maß Phasenumwandlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021160116&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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