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Geometry of contours and Peierls estimates in d=1 Ising models

M. Cassandro·P. A. Ferrari·I. Merola·E. Presutti
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Abstract

Following Fröhlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+α}$, $0\leq α\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.

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M. Cassandro, P. A. Ferrari, I. Merola, E. Presutti. 2002-11-28. Geometry of contours and Peierls estimates in d=1 Ising models. https://doi.org/10.1063/1.1897644

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