1/s-expansion for generalized dimensions in a hierarchical s-state Potts model

Abstract

We consider the s-state Potts model on the diamond hierarchical lattice for large s. We show that the generalized dimensions Dq of the density of zeros supported by the associated Julia set are given by Dq = 1 - (q - 1)|s|-2/3/4 log 2+O(s-1). The information dimension D1 equals 1 to all orders.