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A finite-volume version of Aizenman-Higuchi theorem for the 2d Ising model

Coquille, Loren ; Velenik, Yvan

In: Probability Theory and Related Fields, 2012, vol. 153, no. 1-2, p. 25-44

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    Titre
    • A finite-volume version of Aizenman-Higuchi theorem for the 2d Ising model
    Auteur
    • Coquille, Loren. Department of Mathematics, University of Geneva, 2-4 rue du Lièvre, Case Postale 64, 1211, Geneva 4, Switzerland
    • Velenik, Yvan. Department of Mathematics, University of Geneva, 2-4 rue du Lièvre, Case Postale 64, 1211, Geneva 4, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Probability Theory and Related Fields, 2012, vol. 153, no. 1-2, p. 25-44. Springer-Verlag
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:314463
    Summary
    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