A Nontrivial Renormalization Group Fixed Point for the Dyson–Baker Hierarchical Model

for the Dyson{Baker Hierarchical Model Hans Koch 1 Department of Mathematics, University of Texas at Austin Austin, TX 78712 Peter Wittwer 2 D epartement de Physique Th eorique, Universit e de Gen eve Gen eve, CH 1211 Abstract. We prove the existence of a nontrivial Renormalization Group (RG) xed point for the Dyson{Baker hierarchical model in d = 3 dimensions. The single spin distribution of the xed point is shown to be entire analytic, and bounded by exp( const t6) for large real values of the spin t. Our proof is based on estimates for the zeros of a RG xed point for Gallavotti's hierarchical model. We also present some general results for the heat ow on a space of entire functions, including an order preserving property for zeros, which is used in the RG analysis.