Statistical mechanics of disordered systems: a mathematical perspective
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2006
|
| Ausgabe: | First published |
| Schriftenreihe: | Cambridge series on statistical and probabilistic mathematics
[18] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | xiv, 312 Seiten Illustrationen |
| ISBN: | 9780521849913 9780511616808 0521849918 9781107405332 |
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Datensatz im Suchindex
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| adam_text | STATISTICAL MECHANICS OF DISORDERED SYSTEMS A MATHEMATICAL PERSPECTIVE
ANTON BOVIER WEIERSTRAFI-INSTITUT FIIR ANGEWANDTE ANALYSIS UND
STOCHASTIK, BERLIN AND INSTITUT FIIR MATHEMATIK, TECHNISCHE UNIVERSITDT
BERLIN CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE IX NOMENCLATURE
XIII PART I STATISTICAL MECHANICS 1 1 INTRODUCTION 3 1.1 THERMODYNAMICS
4 2 PRINCIPLES OF STATISTICAL MECHANICS 9 2.1 THE IDEAL GAS IN ONE
DIMENSION 9 2.2 THE MICRO-CANONICAL ENSEMBLE 13 2.3 THE CANONICAL
ENSEMBLE AND THE GIBBS MEASURE 19 2.4 NON-IDEAL GASES IN THE CANONICAL
ENSEMBLE 22 2.5 EXISTENCE OF THE THERMODYNAMIC LIMIT 24 2.6 THE
LIQUID-VAPOUR TRANSITION AND THE VAN DER WAALS GAS 28 2.7 THE GRAND
CANONICAL ENSEMBLE 31 3 LATTICE GASES AND SPIN SYSTEMS 33 3.1 LATTICE
GASES 33 3.2 SPIN SYSTEMS 34 3.3 SUBADDITIVITY AND THE EXISTENCE OF THE
FREE ENERGY 36 3.4 THE ONE-DIMENSIONAL ISING MODEL 37 3.5 THE
CURIE-WEISS MODEL 39 4 GIBBSIAN FORMALISM FOR LATTICE SPIN SYSTEMS 49
4.1 SPIN SYSTEMS AND GIBBS MEASURES 49 4.2 REGULAR INTERACTIONS 52 4.3
STRUCTURE OF GIBBS MEASURES: PHASE TRANSITIONS 59 5 CLUSTER EXPANSIONS
73 5.1 HIGH-TEMPERATURE EXPANSIONS 73 5.2 POLYMER MODELS: THE
DOBRUSHIN-KOTECKY-PREISS CRITERION 76 5.3 CONVERGENCE OF THE
HIGH-TEMPERATURE EXPANSION 82 5.4 LOW-TEMPERATURE EXPANSIONS 88 VIII
CONTENTS PART II DISORDERED SYSTEMS: LATTICE MODELS 95 6 GIBBSIAN
FORMALISM AND METASTATES 97 6.1 INTRODUCTION 97 6.2 RANDOM GIBBS
MEASURES AND METASTATES 99 6.3 REMARKS ON UNIQUENESS CONDITIONS 106 6.4
PHASE TRANSITIONS 107 6.5 THE EDWARDS-ANDERSON MODEL 109 7 THE
RANDOM-FIELD ISING MODEL 111 7.1 THE IMRY-MA ARGUMENT 111 7.2 ABSENCE OF
PHASE TRANSITIONS: THE AIZENMAN-WEHR METHOD 118 7.3 THE
BRICMONT-KUPIAINEN RENORMALIZATION GROUP 125 PART III DISORDERED
SYSTEMS: MEAN-FIELD MODELS 159 8 DISORDERED MEAN-FIELD MODELS 161 9 THE
RANDOM ENERGY MODEL 165 9.1 GROUND-STATE ENERGY AND FREE ENERGY 165 9.2
FLUCTUATIONS AND LIMIT THEOREMS 169 9.3 THE GIBBS MEASURE 175 9.4 THE
REPLICA OVERLAP 180 9.5 MULTI-OVERLAPS AND GHIRLANDA-GUERRA RELATIONS
182 10 DERRIDA S GENERALIZED RANDOM ENERGY MODELS 186 10.1 THE STANDARD
GREM AND POISSON CASCADES 186 10.2 MODELS WITH CONTINUOUS HIERARCHIES:
THE CREM 195 10.3 CONTINUOUS STATE BRANCHING AND COALESCENT PROCESSES
207 11 THE SK MODELS AND THE PARISI SOLUTION 218 11.1 THE EXISTENCE OF
THE FREE ENERGY 218 11.2 2ND MOMENT METHODS IN THE SK MODEL . 220 11.3
THE PARISI SOLUTION AND GUERRA S BOUNDS 227 11.4 THE GHIRLANDA-GUERRA
RELATIONS IN THE SK MODELS 238 11.5 APPLICATIONS IN THE /?-SPIN SK MODEL
240 12 HOPFIELD MODELS 247 12.1 ORIGINS OF THE MODEL 247 12.2 BASIC
IDEAS: FINITE M 250 12.3 GROWING M 257 12.4 THE REPLICA SYMMETRIC
SOLUTION 265 13 THE NUMBER PARTITIONING PROBLEM 285 13.1 NUMBER
PARTITIONING AS A SPIN-GLASS PROBLEM 285 13.2 AN EXTREME VALUE THEOREM
287 13.3 APPLICATION TO NUMBER PARTITIONING 289 REFERENCES 297 INDEX 309
|
| adam_txt |
STATISTICAL MECHANICS OF DISORDERED SYSTEMS A MATHEMATICAL PERSPECTIVE
ANTON BOVIER WEIERSTRAFI-INSTITUT FIIR ANGEWANDTE ANALYSIS UND
STOCHASTIK, BERLIN AND INSTITUT FIIR MATHEMATIK, TECHNISCHE UNIVERSITDT
BERLIN CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE IX NOMENCLATURE
XIII PART I STATISTICAL MECHANICS 1 1 INTRODUCTION 3 1.1 THERMODYNAMICS
4 2 PRINCIPLES OF STATISTICAL MECHANICS 9 2.1 THE IDEAL GAS IN ONE
DIMENSION 9 2.2 THE MICRO-CANONICAL ENSEMBLE 13 2.3 THE CANONICAL
ENSEMBLE AND THE GIBBS MEASURE 19 2.4 NON-IDEAL GASES IN THE CANONICAL
ENSEMBLE 22 2.5 EXISTENCE OF THE THERMODYNAMIC LIMIT 24 2.6 THE
LIQUID-VAPOUR TRANSITION AND THE VAN DER WAALS GAS 28 2.7 THE GRAND
CANONICAL ENSEMBLE 31 3 LATTICE GASES AND SPIN SYSTEMS 33 3.1 LATTICE
GASES 33 3.2 SPIN SYSTEMS 34 3.3 SUBADDITIVITY AND THE EXISTENCE OF THE
FREE ENERGY 36 3.4 THE ONE-DIMENSIONAL ISING MODEL 37 3.5 THE
CURIE-WEISS MODEL 39 4 GIBBSIAN FORMALISM FOR LATTICE SPIN SYSTEMS 49
4.1 SPIN SYSTEMS AND GIBBS MEASURES 49 4.2 REGULAR INTERACTIONS 52 4.3
STRUCTURE OF GIBBS MEASURES: PHASE TRANSITIONS 59 5 CLUSTER EXPANSIONS
73 5.1 HIGH-TEMPERATURE EXPANSIONS 73 5.2 POLYMER MODELS: THE
DOBRUSHIN-KOTECKY-PREISS CRITERION 76 5.3 CONVERGENCE OF THE
HIGH-TEMPERATURE EXPANSION 82 5.4 LOW-TEMPERATURE EXPANSIONS 88 VIII
CONTENTS PART II DISORDERED SYSTEMS: LATTICE MODELS 95 6 GIBBSIAN
FORMALISM AND METASTATES 97 6.1 INTRODUCTION 97 6.2 RANDOM GIBBS
MEASURES AND METASTATES 99 6.3 REMARKS ON UNIQUENESS CONDITIONS 106 6.4
PHASE TRANSITIONS 107 6.5 THE EDWARDS-ANDERSON MODEL 109 7 THE
RANDOM-FIELD ISING MODEL 111 7.1 THE IMRY-MA ARGUMENT 111 7.2 ABSENCE OF
PHASE TRANSITIONS: THE AIZENMAN-WEHR METHOD 118 7.3 THE
BRICMONT-KUPIAINEN RENORMALIZATION GROUP 125 PART III DISORDERED
SYSTEMS: MEAN-FIELD MODELS 159 8 DISORDERED MEAN-FIELD MODELS 161 9 THE
RANDOM ENERGY MODEL 165 9.1 GROUND-STATE ENERGY AND FREE ENERGY 165 9.2
FLUCTUATIONS AND LIMIT THEOREMS 169 9.3 THE GIBBS MEASURE 175 9.4 THE
REPLICA OVERLAP 180 9.5 MULTI-OVERLAPS AND GHIRLANDA-GUERRA RELATIONS
182 10 DERRIDA'S GENERALIZED RANDOM ENERGY MODELS 186 10.1 THE STANDARD
GREM AND POISSON CASCADES 186 10.2 MODELS WITH CONTINUOUS HIERARCHIES:
THE CREM 195 10.3 CONTINUOUS STATE BRANCHING AND COALESCENT PROCESSES
207 11 THE SK MODELS AND THE PARISI SOLUTION 218 11.1 THE EXISTENCE OF
THE FREE ENERGY 218 11.2 2ND MOMENT METHODS IN THE SK MODEL . 220 11.3
THE PARISI SOLUTION AND GUERRA'S BOUNDS 227 11.4 THE GHIRLANDA-GUERRA
RELATIONS IN THE SK MODELS 238 11.5 APPLICATIONS IN THE /?-SPIN SK MODEL
240 12 HOPFIELD MODELS 247 12.1 ORIGINS OF THE MODEL 247 12.2 BASIC
IDEAS: FINITE M 250 12.3 GROWING M 257 12.4 THE REPLICA SYMMETRIC
SOLUTION 265 13 THE NUMBER PARTITIONING PROBLEM 285 13.1 NUMBER
PARTITIONING AS A SPIN-GLASS PROBLEM 285 13.2 AN EXTREME VALUE THEOREM
287 13.3 APPLICATION TO NUMBER PARTITIONING 289 REFERENCES 297 INDEX 309 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T14:54:52Z |
| indexdate | 2024-07-09T20:40:12Z |
| institution | BVB |
| isbn | 9780521849913 9780511616808 0521849918 9781107405332 |
| language | English |
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| physical | xiv, 312 Seiten Illustrationen |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge University Press |
| record_format | marc |
| series | Cambridge series on statistical and probabilistic mathematics |
| series2 | Cambridge series on statistical and probabilistic mathematics |
| spelling | Bovier, Anton 1957- (DE-588)109223829 aut Statistical mechanics of disordered systems a mathematical perspective Anton Bovier: Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin First published Cambridge Cambridge University Press 2006 xiv, 312 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Cambridge series on statistical and probabilistic mathematics [18] Hier auch später erschienene, unveränderte Nachdrucke Mécanique statistique Mécanique statistique ram Ordre et désordre (physique) ram Probabilités Statistique mathématique Statistique mathématique ram Théorie des systèmes Mathematical statistics Probabilities Statistical mechanics System theory Ungeordnetes System (DE-588)4124353-5 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 s Statistische Mechanik (DE-588)4056999-8 s Mathematische Physik (DE-588)4037952-8 s DE-604 Erscheint auch als Online-Ausgabe 978-0-511-61680-8 Cambridge series on statistical and probabilistic mathematics [18] (DE-604)BV011442366 18 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014839742&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bovier, Anton 1957- Statistical mechanics of disordered systems a mathematical perspective Cambridge series on statistical and probabilistic mathematics Mécanique statistique Mécanique statistique ram Ordre et désordre (physique) ram Probabilités Statistique mathématique Statistique mathématique ram Théorie des systèmes Mathematical statistics Probabilities Statistical mechanics System theory Ungeordnetes System (DE-588)4124353-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4124353-5 (DE-588)4056999-8 (DE-588)4037952-8 |
| title | Statistical mechanics of disordered systems a mathematical perspective |
| title_auth | Statistical mechanics of disordered systems a mathematical perspective |
| title_exact_search | Statistical mechanics of disordered systems a mathematical perspective |
| title_exact_search_txtP | Statistical mechanics of disordered systems a mathematical perspective |
| title_full | Statistical mechanics of disordered systems a mathematical perspective Anton Bovier: Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin |
| title_fullStr | Statistical mechanics of disordered systems a mathematical perspective Anton Bovier: Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin |
| title_full_unstemmed | Statistical mechanics of disordered systems a mathematical perspective Anton Bovier: Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin and Institut für Mathematik, Technsiche Universität Berlin |
| title_short | Statistical mechanics of disordered systems |
| title_sort | statistical mechanics of disordered systems a mathematical perspective |
| title_sub | a mathematical perspective |
| topic | Mécanique statistique Mécanique statistique ram Ordre et désordre (physique) ram Probabilités Statistique mathématique Statistique mathématique ram Théorie des systèmes Mathematical statistics Probabilities Statistical mechanics System theory Ungeordnetes System (DE-588)4124353-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mécanique statistique Ordre et désordre (physique) Probabilités Statistique mathématique Théorie des systèmes Mathematical statistics Probabilities Statistical mechanics System theory Ungeordnetes System Statistische Mechanik Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014839742&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011442366 |
| work_keys_str_mv | AT bovieranton statisticalmechanicsofdisorderedsystemsamathematicalperspective |