Geodesic
Ising interfaces and free boundary conditions
Hongler, Clément1 ; Kytölä, Kalle2
1 Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
2 Department of Mathematics and Statistics, P.O. Box 68, FIN–00014 University of Helsinki, Finland
Journal of the American Mathematical Society, Tome 26 (2013) no. 4, pp. 1107-1189

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-2013-00774-2

Hongler, Clément 1 ; Kytölä, Kalle 2

1 Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
2 Department of Mathematics and Statistics, P.O. Box 68, FIN–00014 University of Helsinki, Finland 
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Hongler, Clément; Kytölä, Kalle. Ising interfaces and free boundary conditions. Journal of the American Mathematical Society, Tome 26 (2013) no. 4, pp. 1107-1189. doi: 10.1090/S0894-0347-2013-00774-2

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