A nontrivial Renormalization Group fixed point for the Dyson-Baker hierarchical model |
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Authors: | Hans Koch Peter Wittwer |
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Institution: | (1) Department of Mathematics, University of Texas at Austin, 78712 Austin, TX, USA;(2) Département de Physique Théorique, Université de Genève, CH 1211 Genève, Switzerland |
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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×t
6) 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.Supported in Part by the National Science Foundation under Grant No. DMS-9103590.Supported in Part by the Swiss National Science Foundation. |
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