# Abstract

A Finite-Volume Version of Aizenman-Higuchi Theorem for the 2d Ising Model
L. Coquille, Y. Velenik
Probab. Theory Relat. Fields
153
25-44
(2012).
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 $\beta$ 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: (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.

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.

**Key words:**Ising model, Gibbs states, Aizenman-Higuchi theorem.**Files:**PDF file, Published version, bibtex