A self-avoiding walk exponent bound on the thermal Ising exponent on some hierarchical lattices

Abstract

Calculation of critical exponents on a simple class of hierarchical lattice reveals that lambda s>or= lambda t, where lambda s is the self-avoiding walk fixed point eigenvalue and lambda t the Ising thermal eigenvalue. High-dimensional limits of some families of hierarchies obey lambda t to lambda s as D to infinity ; this convergence replaces the Euclidean concept of upper critical dimension on these lattices. However, families of hierarchies for which D to infinity but with constant connectivity do not show this convergence.