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Title

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

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Published in Probability Theory and Related Fields. 2012, vol. 153, p. 25-44
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 modelGibbs statesTranslation invariance
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arXiv: 1003.6034
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COQUILLE, Loren, VELENIK, Yvan Alain. 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. https://archive-ouverte.unige.ch/unige:6352

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Deposited on : 2010-04-26

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