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On local behaviour of the phase separation line in the 2D Ising model
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  • Published: January 1998

On local behaviour of the phase separation line in the 2D Ising model

  • Ostap Hryniv1 

Probability Theory and Related Fields volume 110, pages 91–107 (1998)Cite this article

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Summary.

The aim of this note is to discuss some statistical properties of the phase separation line in the 2D low-temperature Ising model. We prove the functional central limit theorem for the probability distributions describing fluctuations of the phase boundary in the direction orthogonal to its orientation. The limiting Gaussian measure corresponds to a scaled Brownian bridge with direction dependent parameters. Up to the temperature factor, the variances of local increments of this limiting process are inversely proportional to the stiffness.

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Authors and Affiliations

  1. Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova 3“b”, Lviv 290601, Ukraine; e-mail: hryniv@mebm.lviv.ua, , , , , , UA

    Ostap Hryniv

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  1. Ostap Hryniv
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Received: 6 June 1997/In revised form: 20 August 1997

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Hryniv, O. On local behaviour of the phase separation line in the 2D Ising model. Probab Theory Relat Fields 110, 91–107 (1998). https://doi.org/10.1007/s004400050146

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  • Issue Date: January 1998

  • DOI: https://doi.org/10.1007/s004400050146

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  • AMS Subject Classification (1991): Primary 82B24
  • 82B20; Secondary 60F17
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