Critical interfaces and duality in the Ashkin Teller model

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.

5 pages, 4 figures

References in corpus (12)

• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
• Critical curves in conformally invariant statistical systems
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries
• Critical exponents of domain walls in the two-dimensional Potts model
• Loop models and their critical points
• The Gaussian free field and SLE(4) on doubly connected domains
• SLE in self-dual critical Z(N) spin systems: CFT predictions
• Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model
• Numerical study on Schramm-Loewner Evolution in nonminimal conformal field theories
• Discrete holomorphic parafermions in the Ashkin-Teller model and SLE
• Critical interfaces of the Ashkin-Teller model at the parafermionic point
• Critical domain walls in the Ashkin-Teller model

Cited by in corpus (8)

• Revisiting the combinatorics of the 2D Ising model
• Phase separation and interface structure in two dimensions from field theory
• The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models
• $U_q({\mathfrak{sl}}_n)$ web models and ${\mathbb{Z}}_n$ spin interfaces
• Spin interfaces in the Ashkin-Teller model and SLE
• $U_{\mathfrak{q}}({\mathfrak{sl}}_3)$ web models: Locality, phase diagram and geometrical defects
• Bipartite dimer representation of squared 2d-Ising correlations
• Spin interfaces and crossing probabilities of spin clusters in parafermionic models