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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Ising interfaces and free boundary conditions
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by Clément Hongler and Kalle Kytölä PDF
J. Amer. Math. Soc. 26 (2013), 1107-1189 Request permission

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
  • 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.
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 26 (2013), 1107-1189
  • MSC (2010): Primary 30G25, 60D05, 60F17, 82B20, 82B27; Secondary 60H05
  • DOI: https://doi.org/10.1090/S0894-0347-2013-00774-2
  • MathSciNet review: 3073886