Critical interfaces of the Ashkin-Teller model at the parafermionic point

Abstract

We present an extensive study of interfaces defined in the Z_4 spin lattice representation of the Ashkin-Teller (AT) model. In particular, we numerically compute the fractal dimensions of boundary and bulk interfaces at the Fateev-Zamolodchikov point. This point is a special point on the self-dual critical line of the AT model and it is described in the continuum limit by the Z_4 parafermionic theory. Extending on previous analytical and numerical studies [10,12], we point out the existence of three different values of fractal dimensions which characterize different kind of interfaces. We argue that this result may be related to the classification of primary operators of the parafermionic algebra. The scenario emerging from the studies presented here is expected to unveil general aspects of geometrical objects of critical AT model, and thus of c=1 critical theories in general.

15 pages, 3 figures

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• Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model
• The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models
• Critical interfaces and duality in the Ashkin Teller model
• Discrete holomorphic parafermions in the Ashkin-Teller model and SLE
• Spin interfaces in the Ashkin-Teller model and SLE
• Critical domain walls in the Ashkin-Teller model
• Boundary critical phenomena in the quantum Ashkin-Teller model
• Spin interfaces and crossing probabilities of spin clusters in parafermionic models