The RG-transformation for the hierarchical model
Part of the Lecture Notes in Physics book series (LNP, volume 74)
Part I. Heuristics
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KeywordsCritical Temperature Renormalization Group Central Limit Theorem Hierarchical Model Critical Index
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The Hierarchical Model has been invented by Dyson to show that one-dimensional systems may exhibit phase transitions if they have long-range forces.
Baker reinvented the model and pointed out that the RG acted on the single spin distribution. He also calculated critical indices.
The first rigorous mathematical work was done in the paper by Bleher and Sinai , on the case of Gaussian fixedpoint (with 21/2 < c < 2). The situation at that point was then clarified and reviewed in the following papers.
- G. GALLAVOTTI, H. KNOPS: The Hierarchical Model and the renormalization group. Nuovo Cimento 5, 341–368 (1975).Google Scholar
© Springer-Verlag 1978