FERROMAGNETIC POTTS MODEL ON A HIERARCHICAL LATTICE WITH RANDOM LAYERED INTERACTIONS

We analyze the critical behavior of a q-state Potts model with correlated disordered ferromagnetic exchange interactions along the layers of a diamond hierarchical lattice. For a special class of weakly disordered distributions, we use the topological properties of the lattice to write a set of recursion relations for the moments of the probability distribution of the interaction parameters. We identify a small parameter, q-q0, where q0=0.537…, to expand and decouple the recursion relations. For q<q0, there is just a trivial stable fixed point, associated with the critical behavior of the uniform model. For q>q0 (that correponds, in a uniform case, to a specific heat critical exponent α>-2), the existence of a stable disordered fixed point indicates a change in the critical behavior. We make some remarks on the validity of the Harris criterion for hierarchical lattices.