  We study geometrical properties of interfaces in the random-temperature
q-states Potts model as an example of a conformal field theory weakly perturbed
by quenched disorder. Using conformal perturbation theory in q-2 we compute the
fractal dimension of Fortuin Kasteleyn domain walls. We also compute it
numerically both via the Wolff cluster algorithm for q=3 and via
transfer-matrix evaluations. We obtain numerical results for the fractal
dimension of spin cluster interfaces for q=3. These are found numerically
consistent with the duality kappa(spin) * kappa(FK)= 16 as expressed in
putative SLE parameters.
