This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
The Hierarchical Model has been invented by Dyson to show that one-dimensional systems may exhibit phase transitions if they have long-range forces.
F.J. DYSON: Existence of a phase-transition in a one-dimensional Ising ferromagnet. Commun. Math.Phys. 12, 91 (1969).
F.J.DYSON: An Ising ferromagnet with discontinuous longrange order. Commun. Math. Phys. 21, 269 (1971).
Baker reinvented the model and pointed out that the RG acted on the single spin distribution. He also calculated critical indices.
G.A. BAKER, Jr: Ising model with a scaling interaction. Phys. Rev. B5, 2622, (1972)
G.A. BAKER, Jr; G.R. GOLNER: Spin-spin correlations in an Ising model for which scaling is exact. Phys. Rev. Lett. 31, 22 (1973).
G.A. BAKER, Jr, S. KRINSKY: Renormalization group structure for translationally invariant ferromagnets. Journ. math. Phys. 18, 590 (1977).
The first rigorous mathematical work was done in the paper by Bleher and Sinai [5], 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).
H. van BEYEREN, G. GALLAVOTTI, H. KNOPS: Conservation laws in the Hierarchical Model. Physica 78, 541 (1974).
Rights and permissions
Copyright information
© 1978 Springer-Verlag
About this chapter
Cite this chapter
(1978). The RG-transformation for the hierarchical model. In: A Renormalization Group Analysis of the Hierarchical Model in Statistical Mechanics. Lecture Notes in Physics, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017110
Download citation
DOI: https://doi.org/10.1007/BFb0017110
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08670-3
Online ISBN: 978-3-540-35899-2
eBook Packages: Springer Book Archive