Stochastic processes on a lattice and Gibbs measures:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Dordrecht [u.a.]
Kluwer
1991
|
| Series: | Mathematical physics studies
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 205 - 216 |
| Physical Description: | IX, 220 S. |
| ISBN: | 0792310691 |
Staff View
MARC
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| 240 | 1 | 0 | |a Processus sur un réseau et mesures de Gibbs |
| 245 | 1 | 0 | |a Stochastic processes on a lattice and Gibbs measures |c Bernard Prum and Jean Claude Fort |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1991 | |
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical physics studies |v 11 | |
| 500 | |a Literaturverz. S. 205 - 216 | ||
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Ising model | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Markov processes | |
| 650 | 4 | |a Mathematical physics | |
| 650 | 4 | |a Phase transformations (Statistical physics) | |
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Record in the Search Index
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| adam_text | Contents
Introduction vii
Chapter 1 — Aspects of the Ising Model 1
1. Introduction 1
2. Peierls s Argument 4
3. Imposed Field, Thermodynamic Quantities 8
4. The Unidimensional Case and Tree 12
5. Antiferromagnetism 17
Chapter 2 — Gibbs Measures 19
1. The DLR Problem 19
2. The Structure of ^ 26
3. Gibbs Specifications, Gibbs Measures 31
4. Relations with Thermodynamics 37
Chapter 3 — The Existence of Gibbs Measures .40
1. Markovian Properties 40
2. Existence of Gibbs Measures when $ is Finite 43
3. Existence of Gibbs Measures — the General Case 45
4. Models of the P( p) Type, Gaussian Gibbs Measures 53
Chapter 4 — Phase Transitions — 1: Methods of Convex Analysis 58
1. Holley s Inequality 60
2. The FKG Inequality 63
3. Attracting Specifications .65
4. The Ising Model on Z2.... 68
5. Symmetry Breaking on Zd for d 3 77
Chapter S Other Inequalities .82
1. Ursell Functions .82
2. GKS Inequalities 83
3. The GHS Inequality .90
4. The Simon Lieb Inequality 92
5. Additional Inequalities 97
vi PROCESSES ON A LATTICE AND GIBBS MEASURES
Chapter 6 — Phase Transitions — 2 : Phase Diagrams and Perturbed
Hamiltonians 99
1. Fundamental Configurations 99
2. Perturbed Hamiltonians 102
3. The Pirogov Sinai Theorem 110
4. Boundary Models 112
5. Principle of the Proof 118
Chapter 7 Phase Transitions 3: Positive Reflexivity 120
1. Reflexive Positivity 120
2. The Unidimensional Case 123
3. Checkerboard Estimate 127
4. Gaussian Domination 131
5. The Infrared Domination 132
Chapter 8 — Continuous Symmetry and Other Methods 136
1. The Case of Continuous Symmetry 136
2. The Lack of Symmetry Breaking when d = 2 139
3. Spontaneous Magnetization when d 3 145
4. Onsager s Method 146
5. Combinatorial Approach. 154
6. The Lee Yang Theorem 157
Chapter 9 — The Dynamics of Ising Systems 161
1. Introduction 161
2. A Finite Number of Sites .164
3. An Infinite Number of Sites 169
Chapter 10 — Statistics and Applications .174
1. Ergodicity 175
2. Statistics 181
3. Image Processing 188
4. Other Applications 201
Bibliography 20S
Index 217
|
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| id | DE-604.BV004569204 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:14:26Z |
| institution | BVB |
| isbn | 0792310691 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002810773 |
| oclc_num | 22733936 |
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| physical | IX, 220 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematical physics studies |
| series2 | Mathematical physics studies |
| spelling | Prum, Bernard Verfasser aut Processus sur un réseau et mesures de Gibbs Stochastic processes on a lattice and Gibbs measures Bernard Prum and Jean Claude Fort Dordrecht [u.a.] Kluwer 1991 IX, 220 S. txt rdacontent n rdamedia nc rdacarrier Mathematical physics studies 11 Literaturverz. S. 205 - 216 Mathematische Physik Ising model Lattice theory Markov processes Mathematical physics Phase transformations (Statistical physics) Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 gnd rswk-swf Gittermodell (DE-588)4226961-1 gnd rswk-swf Phasenumwandlung (DE-588)4132140-6 s Gittermodell (DE-588)4226961-1 s DE-604 Stochastischer Prozess (DE-588)4057630-9 s Fort, Jean C. Verfasser aut Mathematical physics studies 11 (DE-604)BV000006511 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002810773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Prum, Bernard Fort, Jean C. Stochastic processes on a lattice and Gibbs measures Mathematical physics studies Mathematische Physik Ising model Lattice theory Markov processes Mathematical physics Phase transformations (Statistical physics) Stochastischer Prozess (DE-588)4057630-9 gnd Phasenumwandlung (DE-588)4132140-6 gnd Gittermodell (DE-588)4226961-1 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4132140-6 (DE-588)4226961-1 |
| title | Stochastic processes on a lattice and Gibbs measures |
| title_alt | Processus sur un réseau et mesures de Gibbs |
| title_auth | Stochastic processes on a lattice and Gibbs measures |
| title_exact_search | Stochastic processes on a lattice and Gibbs measures |
| title_full | Stochastic processes on a lattice and Gibbs measures Bernard Prum and Jean Claude Fort |
| title_fullStr | Stochastic processes on a lattice and Gibbs measures Bernard Prum and Jean Claude Fort |
| title_full_unstemmed | Stochastic processes on a lattice and Gibbs measures Bernard Prum and Jean Claude Fort |
| title_short | Stochastic processes on a lattice and Gibbs measures |
| title_sort | stochastic processes on a lattice and gibbs measures |
| topic | Mathematische Physik Ising model Lattice theory Markov processes Mathematical physics Phase transformations (Statistical physics) Stochastischer Prozess (DE-588)4057630-9 gnd Phasenumwandlung (DE-588)4132140-6 gnd Gittermodell (DE-588)4226961-1 gnd |
| topic_facet | Mathematische Physik Ising model Lattice theory Markov processes Mathematical physics Phase transformations (Statistical physics) Stochastischer Prozess Phasenumwandlung Gittermodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002810773&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006511 |
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