Towards functional flows for hierarchical models

The recursion relations of hierarchical models are studied and contrasted with functional renormalization group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where the spectrum of universal eigenvalues at criticality is studied. A significant correlation amongst scaling exponents is pointed out and analyzed in view of an underlying optimization. Continuous functional flows are provided which match with high accuracy all known scaling exponents from Dyson’s hierarchical model for discrete block-spin transformations. Implications of the results are discussed.