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

Hryniv, Ostap

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
• Public URL: https://durham-repository.worktribe.com/output/1557734