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A finite-volume version of Aizenman-Higuchi Theorem for the 2d ising Model

Published inProbability theory and related fields, vol. 153, p. 25-44
Publication date2012
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 are convex combinations of the two pure phases. We present here a new approach to this result, with a number of advantages: (i) We obtain a finite-volume, quantitative analogue (implying the classical claim); (ii) the scheme of our proof seems more natural and provides a better picture of the underlying phenomenon; (iii) this new approach seems substantially more robust.

Keywords
  • Ising model
  • Gibbs states
  • Translation invariance
Classification
  • arxiv : math.PR
Citation (ISO format)
COQUILLE, Loren, VELENIK, Yvan. A finite-volume version of Aizenman-Higuchi Theorem for the 2d ising Model. In: Probability theory and related fields, 2012, vol. 153, p. 25–44.
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Identifiers
ISSN of the journal0178-8051
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