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

Hryniv, Ostap

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Abstract

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.

Citation

Hryniv, O. (1998). On local behaviour of the phase separation line in the 2D Ising model. Probability Theory and Related Fields, 110(1), 91-107. https://doi.org/10.1007/s004400050146

Journal Article Type Article
Publication Date Jan 1, 1998
Deposit Date Jun 13, 2014
Publicly Available Date Jun 13, 2014
Journal Probability Theory and Related Fields
Print ISSN 0178-8051
Electronic ISSN 1432-2064
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 110
Issue 1
Pages 91-107
DOI https://doi.org/10.1007/s004400050146

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