Laboratoire de Physique Théorique
Toulouse - UMR 5152

During these last years, many development came with the introduction of the Schramm-Loewner evolution (SLE) which constitutes a family of conformally invariant stochastic growth process. In particular, the SLE approach offers a conceptually new description of certain boundary interfaces defined in the O(n) models. After recalling some of the results obtained, in particular in the case of the Q-states Potts models, I will present results for non minimal conformal field theory where in most cases one needs to rely on numerical results. I will present results for the 3 states Potts model with disorder and for the case of parafermionic spin models.