Critical Interfaces in the Random-Bond Potts Model

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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 (FK) domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We also obtain numerical results for the fractal dimension of spin clusters interfaces for q=3. These are found numerically consistent with the duality kappaspinkappaFK=16 as expressed in putative SLE parameters.