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 β/ν varies continuously with q, assuming non-Ising values for q > 4, whereas the correlation length exponent v 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. © 1998 Elsevier Science B.V