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- Title
A finite-volume version of Aizenman-Higuchi theorem for the 2d Ising model.
- Authors
Coquille, Loren; Velenik, Yvan
- Abstract
In the late 1970s, in two celebrated papers, Aizenman and Higuchi independently established that all infinite-volume Gibbs measures of the two-dimensional ferromagnetic nearest-neighbor Ising model at inverse temperature $${\beta\geq 0}$$ are of the form $${\alpha\mu^{+}_\beta + (1-\alpha)\mu^{-}_\beta}$$ , where $${\mu^{+}_\beta}$$ and $${\mu^{-}_\beta}$$ are the two pure phases and $${0\leq\alpha\leq 1}$$ . We present here a new approach to this result, with a number of advantages: (a) We obtain an optimal finite-volume, quantitative analogue (implying the classical claim); (b) the scheme of our proof seems more natural and provides a better picture of the underlying phenomenon; (c) this new approach might be applicable to systems for which the classical method fails.
- Subjects
ISING model; FINITE volume method; GIBBS phenomenon; MEASURE theory; PROOF theory; SYSTEMS theory; QUANTITATIVE research
- Publication
Probability Theory & Related Fields, 2012, Vol 153, Issue 1/2, p25
- ISSN
0178-8051
- Publication type
Article
- DOI
10.1007/s00440-011-0339-6