A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model

Details A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model

2010-03-31

arxiv.org/abs/1003.6034v3

Mathematics

Probability

A couple of typos corrected. To appear in Probab. Theory Relat. Fields

Scientific paper

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 an optimal 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 might be applicable to systems for which the classical method fails.

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