Lace Expansion for the Ising Model
نویسندگان
چکیده
منابع مشابه
Lace expansion for the Ising model
The lace expansion has been a powerful tool for investigating mean-field behavior for various stochastic-geometrical models, such as self-avoiding walk and percolation, above their respective upper-critical dimension. In this paper, we prove the lace expansion for the Ising model that is valid for any spin-spin coupling. For the ferromagnetic case, we also prove that the expansion coefficients ...
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LACES DEFINITION. Let P be a finite set of properties. A mapping l that Ž . assigns to any subset S ; P another subset l S is called a lace map if, for all S, G, S , S ; P: 1 2 Ž . Ž . i l S ; S; Ž . Ž . Ž . Ž . ii l S ; G ; S « l G s l S ; Ž . Ž . Ž . Ž . Ž . iii l S s l S « l S j S s l S . 1 2 1 2 1 Ž . Ž . Ž . A set L for which l L s L is called a lace. By applying ii to G s l S , Ž Ž .. Ž ....
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David Brydges and Thomas Spencer's Lace Expansion is abstracted, and it is shown how it sometimes gives rise to sieves. LACES Definition: Let P be a finite set of properties. A mapping l that assigns to any subset S ⊂ P another subset l(S), is called a lace-map, A set L for which l(L) = L is called a lace. By applying (ii) to G = l(S), it is seen that l(l(S)) = l(S), for any set of properties S...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2007
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-007-0227-1