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Stochastic processes on a lattice and Gibbs measures

Author: Bernard Prum; Jean Claude Fort
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers, ©1991.
Series: Mathematical physics studies, v. 11.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Bernard Prum; Jean Claude Fort
ISBN: 0792310691 9780792310693
OCLC Number: 22733936
Notes: Translation of: Processus sur un réseau et mesure de Gibbs.
Description: ix, 220 pages : illustrations ; 25 cm.
Contents: 1 - Aspects of the Ising Model.- 1. Introduction.- 2. Peieris's Argument.- 3. Imposed Field, Thermodynamic Quantities.- 4. The Unidimensional Case and Tree.- 5. Antiferromagnetism.- 2 - Gibbs Measures.- 1. The DLR Problem.- 2. The Structure of G.- 3. Gibbs Specifications, Gibbs Measures.- 4. Relations with Thermodynamics.- 3 - The Existence of Gibbs Measures.- 1. Markovian Properties.- 2. Existence of Gibbs Measures when ? is Finite.- 3. Existence of Gibbs Measures - the General Case.- 4. Models of the P(?)-Type, Gaussian Gibbs Measures S.- 4 - Phase Transitions - 1: Methods of Convex Analysis.- 1. Holley's Inequality.- 2. The FKG Inequality.- 3. Attracting Specifications.- 4. The Ising Model on ?2.- 5. Symmetry Breaking on ?d for d ? 3.- 5 - Other Inequalities.- 1. Urse11 Functions.- 2. GK S Inequalities.- 3. The GHS Inequality.- 4. The Simon-Lieb Inequality.- S. Additional Inequalities.- 6 - Phase Transitions - 2: Phase Diagrams and Perturbed Hamiltonians.- 1. Fundamental Configurations.- 2. Perturbed Hamiltonians.- 3. The Pirogov-Sinai Theorem.- 4. Boundary Models.- S. Principle of the Proof.- 7 - Phase Transitions - 3: Positive Reflexivity.- 1. Reflexive Positivity.- 2. The Unidimensional Case.- 3. Checkerboard Estimate.- 4. Gaussian Domination.- 5. The Infrared Domination.- 8 - Continuous Symmetry and Other Methods.- 1. The Case of Continuous Symmetry.- 2. The Lack of Symmetry Breaking when d = 2.- 3. Spontaneous Magnetization when d ? 3.- 4. Onsager s Method.- 5. Combinatorial Approach.- 6. The Lee-Yang Theorem.- 9 - The Dynamics of Ising Systems.- 1. Introduction.- 2. A Finite Number of Sites.- 3. An Infinite Number of Sites.- 10 - Statistics and Applications.- 1. Ergodicity.- 2. Statistics.- 3. Image Processing.- 4. Other Applications.
Series Title: Mathematical physics studies, v. 11.
Other Titles: Processus sur un réseau et mesure de Gibbs.
Responsibility: Bernard Prum and Jean Claude Fort ; translated by Bertram Eugene Schwarzbach.
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