Universality: Accurate Checks in Dyson's Hierarchical Model

摘要

In this talk we present high-accuracy calculations of the susceptibility near β_c for Dyson's hierarchical model in D = 3. Using linear fitting, we estimate the leading (γ) and subleading (Δ) exponents. Independent estimates are obtained by calculating the first two eigenvalues of the linearized renormalization group transformation. We found γ = 1.29914073 ± 10~(-8) and, Δ = 0.4259469 ± 10~(-7) independently of the choice of local integration measure (Ising or Landau-Ginzburg). After a suitable rescaling, the approximate fixed points for a large class of local measure coincide accurately with a fixed point constructed by Koch and Wittwer.