  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 eta_n for several moments,
n, of the correlation functions, including typical (n -> 0), average (n=1) and
others. In addition, for q=8, we find that there is only a single correlation
length exponent describing the correlation length away from criticality. This
is numerically very close to the pure Ising value of unity.
