Critical interfaces and duality in the Ashkin Teller model

TL;DR

This paper investigates the fractal properties and duality relations of spin interfaces and FK cluster boundaries in the Ashkin-Teller model at criticality, revealing multiple fractal dimensions and a duality consistent with extended conformal field theory.

Contribution

It provides the first numerical evidence of duality relations for FK cluster boundaries in the Ashkin-Teller model across its critical line.

Findings

Fractal dimension of spin interfaces can take four different values.

Spin interfaces with fractal dimension d_f=3/2 are observed along the critical line.

FK cluster boundary dimensions satisfy a duality relation with their outer boundaries.

Abstract

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