عنوان

Stochastic Processes on a Lattice and Gibbs Measures

(Number (ISBN

9401054428

(Number (ISBN

9401132682

(Number (ISBN

9789401054423

(Number (ISBN

9789401132688

Number

b595811

Title Proper

Stochastic Processes on a Lattice and Gibbs Measures

General Material Designation

[Book]

First Statement of Responsibility

by Bernard Prum, Jean Claude Fort.

Place of Publication, Distribution, etc.

Dordrecht

Name of Publisher, Distributor, etc.

Springer Netherlands

Date of Publication, Distribution, etc.

1991

Series Title

Mathematical Physics Studies, A Supplementary Series to Letter in Mathematical Physics, 11

Text of Note

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.

Class number

Book number

by Bernard Prum, Jean Claude Fort.

Bernard Prum

Jean Claude Fort

Electronic name

[Book]

Y