Critical interfaces in the random-bond Potts model

Jesper L. Jacobsen (1) , Pierre Le Doussal (1) , Marco Picco (2) , Raoul Santachiara (1) , Kay Joerg Wiese (1)

1 LPTENS - Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure]
2 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Domaines: Autre [cond-mat.other]

Jesper L. Jacobsen, Pierre Le Doussal, Marco Picco, Raoul Santachiara, Kay Joerg Wiese. Critical interfaces in the random-bond Potts model. Physical Review Letters, 2009, 102, pp.070601. ⟨hal-00325252⟩