Critical interfaces and duality in the Ashkin Teller model

Marco Picco (1) , Raoul Santachiara (2)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

We report on the numerical measures on different spin interfaces and FK cluster boundaries in the Askhin-Teller (AT) model. For a general point on the AT critical line, we find that the fractal dimension of a generic spin cluster interface can take one of four different possible values. In particular we found spin interfaces whose fractal dimension is d_f=3/2 all along the critical line. Further, the fractal dimension of the boundaries of FK clusters were found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides a clear numerical evidence that such duality, which is well known in the case of the O(n) model, exists in a extended CFT.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Marco Picco, Raoul Santachiara. Critical interfaces and duality in the Ashkin Teller model. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2011, 83, pp.61124. ⟨10.1103/PhysRevE.83.061124⟩. ⟨hal-00533081⟩