Holdings: Gibbs measures and phase transitions

Gibbs measures and phase transitions:

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Bibliographic Details
Main Author:	Georgii, Hans-Otto 1944-2017 (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] de Gruyter 2011
Edition:	2. ed.
Series:	De Gruyter studies in mathematics 9
Subjects:	Gibbs-Maß Phasenumwandlung
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. [495] - 537
Physical Description:	XIV, 545 S.
ISBN:	9783110250299

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MARC


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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
author_GND	(DE-588)10807546X
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	519 - Probabilities and applied mathematics
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dewey-search	519.2
dewey-sort	3519.2
dewey-tens	510 - Mathematics
discipline	Physik Mathematik
edition	2. ed.
format	Book
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indexdate	2024-07-09T22:54:22Z
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isbn	9783110250299
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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
volume_link	(DE-604)BV000005407
work_keys_str_mv	AT georgiihansotto gibbsmeasuresandphasetransitions

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