Ising Interfaces and Free Boundary Conditions

Details Ising Interfaces and Free Boundary Conditions Ising Interfaces and Free Boundary Conditions

2011-08-02

arxiv.org/abs/1108.0643v2

Mathematics

Probability

82 pages, 28 figures. Replaces the shorter version, in particular to include discrete complex analysis details

Scientific paper

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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