Spin interfaces in the Ashkin-Teller model and SLE

Details Spin interfaces in the Ashkin-Teller model and SLE Spin interfaces in the Ashkin-Teller model and SLE

2011-11-14

arxiv.org/abs/1111.3197v1

J. Stat. Mech. (2012) P01012

Physics

Condensed Matter

Statistical Mechanics

12 pages, 6 figures

Scientific paper

10.1088/1742-5468/2012/01/P01012

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.

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