Accurate Checks of Universality for Dyson's Hierarchical Model

Using recently developed methods, we perform high-accuracy calculations ofthe susceptibility near beta_c for the D=3 version of Dyson's hierarchicalmodel. Using linear fits, we estimate the leading gamma and subleading Deltaexponents. Independent estimates are obtained by calculating the first twoeigenvalues of the linearized renormalization group transformation. We foundgamma = 1.29914073 (with an estimated error of 10^{-8}) and, Delta=0.4259469(with an estimated error of 10^{-7}) independently of the choice of localintegration measure (Ising or Landau-Ginzburg). After a suitable rescaling, theapproximate fixed points for a large class of local measure coincide accuratelywith a fixed point constructed by Koch and Wittwer.Comment: 9 pages, Revtex, 1 figur