2010/03/31 by Loren Coquille, Yvan Velenik
Mathematics · Physics and Astronomy · #math.PR #math-ph #math.MP
paper · pdf · doi:10.1007/s00440-011-0339-6
published as Probability Theory and Related Fields, Volume 153, Numbers 1-2, 25-44, 2012 · A couple of typos corrected. To appear in Probab. Theory Relat. Fields
arxiv created 2010/12/22 · arxiv updated 2012/12/11
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.