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Geometry of contours and Peierls estimates in d=1 Ising models | | M. Cassandro
; P.A. Ferrari
; I. Merola
; E. Presutti
; | | Date: |
25 Nov 2002 | | Subject: | Mathematical Physics; Probability MSC-class: 82B | math-ph math.MP math.PR | | Abstract: | Following Fröhlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+alpha}$, $0leq alphaleq 1/2$. 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. | | Source: | arXiv, math-ph/0211062 | | Services: | Forum | Review | PDF | Favorites | |
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