Boundary critical behaviour of two-dimensional random Ising models

Using extensive Monte Carlo simulations, transfer matrix techniques and conformal invariance, ferromagnetic random q-state Potts models for \(\) are studied in the vicinity of the critical temperature. In particular the surface and bulk magnetization exponents \(\) and \(\) are found monotonically increasing with q. At the critical temperature, different moments (n) of the magnetization profiles are calculated which are all found to accurately follow predictions of conformal invariance. The critical correlation functions show multifractal behaviour, the decay exponents of the different moments both in the volume and at the surface, are n-dependent.