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A Renormalization Group Analysis of the Hierarchical Model in Statistical Mechanics

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Author(s): Pierre Collet, Jean-Pierre Eckmann (auth.)
Series: Lecture Notes in Physics 74
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1978

Language: English
Commentary: +OCR
Pages: 202
Tags: Physics, general

Introduction....Pages 1-3
Probabilistic formulation of the problem....Pages 4-7
The RG-transformation for the hierarchical model....Pages 8-18
The existence of a non-trivial fixed point....Pages 19-37
The flow around the fixed point....Pages 38-43
Discussion of the critical indices....Pages 44-58
Global properties of the flow....Pages 59-75
Discussion of the thermodyamic limit....Pages 76-81
Perturbation theory....Pages 82-86
Explicit perturbation calculation for the Eigenvalue λ 2 ....Pages 87-94
Linear problems and the existence of ϕ ε ....Pages 95-116
Differentiability of ø ε ....Pages 117-126
The normal form of the flow....Pages 127-135
Crossover. Part 2....Pages 136-145
Crossover, Part II. A) Single phase region....Pages 146-154
Crossover Part II. B) Two phase region....Pages 155-194
Miscellaneous short proofs....Pages 195-199