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)=1/2log₂(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, x₁→0.192±0.002.