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

TL;DR

This paper investigates the fractal properties of interfaces in the Z_4 spin representation of the Ashkin-Teller model at a special critical point, revealing three distinct fractal dimensions linked to parafermionic operators.

Contribution

It provides the first detailed numerical analysis of boundary and bulk interface fractal dimensions at the Fateev-Zamolodchikov point of the Ashkin-Teller model, connecting them to parafermionic algebra.

Findings

Identified three different fractal dimensions for interfaces.

Linked fractal dimensions to primary operators of the parafermionic algebra.

Enhanced understanding of geometrical structures in critical c=1 theories.

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.