Critical interfaces and duality in the Ashkin-Teller model

We report on the numerical measures on different spin interfaces and Fortuin-Kasteleyn (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. Furthermore, the fractal dimension of the boundaries of FK clusters was found to satisfy all along the AT critical line a duality relation with the fractal dimension of their outer boundaries. This result provides clear numerical evidence that such duality, which is well known in the case of the O(n) model, exists in an extended conformal field theory.