Failure of the Harris criterion for directed polymers on hierarchical lattices

Abstract

Exact real space renormalization group analysis shows that the Harris criterion can be violated for two randomly interacting directed polymers on a hierarchical lattice with branching factor b. The interaction energy when the polymers meet on the same bond is random. For a particular case, we find a negative crossover exponent φ for disorder when b>2, even though the specific heat exponent a is positive for b>2+√2 . Other cases are also considered. General conditions for the validity of the Harris criterion for this system are determined.