  The recursion relations of hierarchical models are studied and contrasted
with functional renormalisation 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 analysed in view of an underlying optimisation. 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.
