Geometry of contours and Peierls estimates in d=1 Ising models with long range interactions | Zendy

M. Cassandro | Zendy; Pablo A. Ferrari | Zendy; Immacolata Merola | Zendy; Errico Presutti | Zendy

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Geometry of contours and Peierls estimates in d=1 Ising models with long range interactions

Author(s) -

M. Cassandro,

Pablo A. Ferrari,

Immacolata Merola,

Errico Presutti

Publication year - 2005

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1897644

Subject(s) - ising model , physics , spin (aerodynamics) , ferromagnetism , ising spin , range (aeronautics) , mathematical physics , phase transition , geometry , theoretical physics , mathematics , quantum mechanics , materials science , composite material , thermodynamics

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systemswith ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$,$0\leq \alpha\leq 1/2$. We introduce a geometric description of the spinconfigurations in terms of triangles which play the role of contours and forwhich we establish Peierls bounds. This in particular yields a direct proof ofthe well known result by Dyson about phase transitions at low temperatures.Comment: 28 pages, 3 figure

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