Ising interfaces and free boundary conditions

Hongler, Clément; Kytölä, Kalle

doi:10.1090/S0894-0347-2013-00774-2

Ising interfaces and free boundary conditions
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by Clément Hongler and Kalle Kytölä

J. Amer. Math. Soc. 26 (2013), 1107-1189

DOI: https://doi.org/10.1090/S0894-0347-2013-00774-2

Published electronically: June 25, 2013

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Abstract:

We study the interfaces arising in the two-dimensional Ising model at critical temperature, without magnetic field. We show that in the presence of free boundary conditions between plus and minus spins, the scaling limit of these interfaces can be described by a variant of SLE, called dipolar SLE(3). This generalizes a celebrated result of Chelkak and Smirnov and proves a conjecture of Bauer, Bernard, and Houdayer. We mention two possible applications of our result.

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