Large-qasymptotics of the random-bond Potts model

Abstract

We numerically examine the large-q asymptotics of the q-state random bond Potts model. Special attention is paid to the parametrization of the critical line, which is determined by combining the loop representation of the transfer matrix with Zamolodchikov's c-theorem. Asymptotically the central charge seems to behave like c(q)=1 / 2 log(2)(q)+O(1). Very accurate values of the bulk magnetic exponent x(1) are then extracted by performing Monte Carlo simulations directly at the critical point. As q-->infinity, these seem to tend to a nontrivial limit, x(1)-->0.192+/-0.002.