On the Ising model with random boundary condition

A.C.D. Enter, van, K. Netocný, H.G. Schaap

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)


    The infinite-volume limit behavior of the 2d Ising model under possibly strong random boundary conditions is studied. The model exhibits chaotic size-dependence at low temperatures and we prove that the + and – phases are the only almost sure limit Gibbs measures, assuming that the limit is taken along a sparse enough sequence of squares. In particular, we provide an argument to show that in a sufficiently large volume a typical spin configuration under a typical boundary condition contains no interfaces. In order to exclude mixtures as possible limit points, a detailed multi-scale contour analysis is performed.
    Original languageEnglish
    Pages (from-to)997-1056
    JournalJournal of Statistical Physics
    Issue number5-6
    Publication statusPublished - 2005


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