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Communications in Mathematical Physics

, Volume 164, Issue 3, pp 627–647 | Cite as

A nontrivial Renormalization Group fixed point for the Dyson-Baker hierarchical model

  • Hans Koch
  • Peter Wittwer
Article

Abstract

We prove the existence of a nontrivial Renormalization Group (RG) fixed point for the Dyson-Baker hierarchical model ind=3 dimensions. The single spin distribution of the fixed point is shown to be entire analytic, and bounded by exp(−const×t6) for large real values of the spint. Our proof is based on estimates for the zeros of a RG fixed point for Gallavotti's hierarchical model. We also present some general results for the heat flow on a space of entire functions, including an order preserving property for zeros, which is used in the RG analysis.

Keywords

Neural Network Statistical Physic Complex System Heat Flow Nonlinear Dynamics 
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References

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    See e. g. Theorem (2.10.3) in: Boas, R.P.: Entire Functions. New York: Academic Press 1954Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Hans Koch
    • 1
  • Peter Wittwer
    • 2
  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA
  2. 2.Département de Physique ThéoriqueUniversité de GenèveGenèveSwitzerland

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