Fluctuations of the phase boundary in the 2D Ising ferromagnet

Dobrushin, R.; Hryniv, O.

Abstract

We discuss some statistical properties of the phase boundary in the 2D low-temperature Ising ferromagnet in a box with the two-component boundary conditions. We prove the weak convergence in C[0,1] of measures describing the fluctuations of phase boundaries in the canonical ensemble of interfaces with fixed endpoints and area enclosed below them. The limiting Gaussian measure coincides with the conditional distribution of certain Gaussian process obtained by the integral transformation of the white noise.

Citation

Dobrushin, R., & Hryniv, O. (1997). Fluctuations of the phase boundary in the 2D Ising ferromagnet. Communications in Mathematical Physics, 189(2), 395-445. https://doi.org/10.1007/s002200050209

• Journal Article Type: Article
• Publication Date: Nov 1, 1997
• Deposit Date: Jun 13, 2014
• Publicly Available Date: Jun 13, 2014
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 189
• Issue: 2
• Pages: 395-445
• DOI: https://doi.org/10.1007/s002200050209
• Public URL: https://durham-repository.worktribe.com/output/1581798