Abstract
We present an extensive study of interfaces defined in theZ4 spin lattice representation of the Ashkin–Teller (AT) model. In particular, wenumerically compute the fractal dimensions of boundary and bulk interfaces at theFateev–Zamolodchikov point. This point is a special point on the self-dual criticalline of the AT model and it is described in the continuum limit by the parafermionic theory. Extending on previous analytical and numerical studies,we point out the existence of three different values of fractal dimensions whichcharacterize different kind of interfaces. We argue that this result may berelated to the classification of primary operators of the parafermionic algebra.The scenario emerging from the studies presented here is expected to unveilgeneral aspects of geometrical objects of the critical AT model, and thus ofc = 1 critical theories in general.
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