Spin interfaces in the Ashkin-Teller model and SLE

Abstract

We investigate the scaling properties of the spin interfaces in the Ashkin-Teller model. These interfaces are a very simple instance of lattice curves coexisting with a fluctuating degree of freedom, which renders the analytical determination of their exponents very difficult. One of our main findings is the construction of boundary conditions which ensure that the interface still satisfies the Markov property in this case. Then, using a novel technique based on the transfer matrix, we compute numerically the left-passage probability, and our results confirm that the spin interface is described by an SLE in the scaling limit. Moreover, at a particular point of the critical line, we describe a mapping of Ashkin-Teller model onto an integrable 19-vertex model, which, in turn, relates to an integrable dilute Brauer model.

12 pages, 6 figures

References in corpus (4)

• SLE in the three-state Potts model - a numerical study
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries
• SLE in self-dual critical Z(N) spin systems: CFT predictions
• Critical interfaces of the Ashkin-Teller model at the parafermionic point

Cited by in corpus (6)

• Phase separation and interface structure in two dimensions from field theory
• On the transition between the disordered and antiferroelectric phases of the 6-vertex model
• The Hintermann-Merlini-Baxter-Wu and the Infinite-Coupling-Limit Ashkin-Teller Models
• Stability and Loop Models from Decohering Non-Abelian Topological Order
• The 16-vertex model and its even and odd 8-vertex subcases on the square lattice
• q-deformed Loewner evolution