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We present an extensive study of interfaces defined in the Z_4 spin latticerepresentation of the Ashkin-Teller (AT) model. In particular, we numericallycompute the fractal dimensions of boundary and bulk interfaces at theFateev-Zamolodchikov point. This point is a special point on the self-dualcritical line of the AT model and it is described in the continuum limit by theZ_4 parafermionic theory. Extending on previous analytical and numericalstudies [10,12], we point out the existence of three different values offractal dimensions which characterize different kind of interfaces. We arguethat this result may be related to the classification of primary operators ofthe parafermionic algebra. The scenario emerging from the studies presentedhere is expected to unveil general aspects of geometrical objects of criticalAT model, and thus of c=1 critical theories in general.

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