Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study

We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting universality classes by combining transfer matrix data with conformal invariance. The magnetic exponent beta/nu varies continuously with q, assuming non-Ising values for q>4, whereas the correlation length exponent nu is numerically consistent with unity. We present evidence for the correctness of a formerly proposed phase diagram, unifying pure, percolative and non-trivial random behaviour.