Following Fröhlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as ∣x−y∣−2+α, 0 ⩽ α ⩽ 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.
Geometry of contours and Peierls estimates in d=1 Ising models with long range interactions
MEROLA, IMMACOLATA;
2005-01-01
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 ⩽ α ⩽ 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.File in questo prodotto:
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