Boundary critical behaviour of two-dimensional random Potts models

Using extensive Monte Carlo simulations, transfer matrix techniques and con formal invariance, ferromagnetic random q-state Potts models for 3 less tha n or equal to q less than or equal to 8 are studied in the vicinity of the critical temperature. In particular the surface and bulk magnetization expo nents beta(1) and beta are found monotonically increasing with q. At the cr itical temperature, different moments (n) of the magnetization profiles are calculated which are all found to accurately follow predictions of conform al invariance. The critical correlation functions show multifractal behavio ur, the decay exponents of the different moments both in the volume and at the surface, are n-dependent.