Large-qasymptotics of the random-bond Potts model

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) =12log₂ (q) +O (1). Very accurate values of the bulk magnetic exponent x₁ are then extracted by performing Monte Carlo simulations directly at the critical point. As q, these seem to tend to a nontrivial limit, x₁0. 1920. 002.