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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Ising interfaces and free boundary conditions


Authors: Clément Hongler and Kalle Kytölä
Journal: J. Amer. Math. Soc. 26 (2013), 1107-1189
MSC (2010): Primary 30G25, 60D05, 60F17, 82B20, 82B27; Secondary 60H05
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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Additional Information

Clément Hongler
Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
Email: hongler@math.columbia.edu

Kalle Kytölä
Affiliation: Department of Mathematics and Statistics, P.O. Box 68, FIN–00014 University of Helsinki, Finland
Email: kalle.kytola@helsinki.fi

DOI: http://dx.doi.org/10.1090/S0894-0347-2013-00774-2
PII: S 0894-0347(2013)00774-2
Received by editor(s): November 4, 2011
Received by editor(s) in revised form: November 7, 2011, and April 4, 2013
Published electronically: June 25, 2013
Additional Notes: This research was partially supported by the Swiss NSF, the European Research Council AG CONFRA, the Academy of Finland, the National Science Foundation under grant DMS-1106588, and the Minerva Foundation.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.