- 93-230 Koch H., Wittwer P.
- A Nontrivial Renormalization Group Fixed Point
for the Dyson-Baker Hierarchical Model
(72K, plain TeX)
Aug 31, 93
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Abstract. We prove the existence of a nontrivial Renormalization Group (RG)
fixed point for the Dyson-Baker hierarchical model in d=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 spin t.
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.