We compute the combined two and three loop order correction to the spin-spin correlation functions for the 2D Ising and q-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach for the perturbation series around the conformal field theories representing the pure models. We obtain corrections for the correlations functions which produce crossover in the amplitude but don't change the critical exponent in the case of the Ising model and which produce a shift in the critical exponent, due to randomness, in the case of the Potts model. Comparison with numerical data is discussed briefly.
We present results of Monte Carlo simulations of random bond Potts models in two dimensions, for different numbers of Potts states q. We introduce a simple scheme which yields continuous self-dual distributions of the interactions. As expected, we find multifractal behavior of the correlation functions at the critical point and obtain estimates of the exponent ${\ensuremath{\eta}}_{n}$ for several moments n of the correlation functions, including typical $(\stackrel{\ensuremath{\rightarrow}}{n}0)$, average
(n=1), and others. In addition, for
q=8, we find that there is only a single correlation length exponent $\ensuremath{\nu}$ describing the correlation length away from criticality. This is numerically very close to the pure Ising value $\ensuremath{\nu}=1$.