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

Abstract

Following Fröhlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y{|}^{-2+\alpha }$, $0\le \alpha \le 1/2$. 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.

28 pages, 3 figures

References in corpus (1)

• Liquid-Vapor Phase Transitions for Systems with Finite Range Interactions

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