02-513 M. Cassandro, P.A. Ferrari, I. Merola, E. Presutti

Geometry of contours and Peierls estimates in d=1 Ising models with long range interactions (147K, LaTeX 2e with 2 PS Figures) Dec 11, 02

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Abstract. Following Fr\"ohlich and Spencer, \cite{FS}, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. 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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