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Lace Expansion for the Ising Model

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タイトル: Lace Expansion for the Ising Model
著者: Sakai, Akira 著作を一覧する
発行日: 2007年
出版者: Springer
誌名: Communications in Mathematical Physics
巻: 272
号: 2
開始ページ: 283
終了ページ: 344
出版社 DOI: 10.1007/s00220-007-0227-1
抄録: 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 obey certain diagrammatic bounds that are similar to the diagrammatic bounds on the lace-expansion coefficients for self-avoiding walk. As a result, we obtain Gaussian asymptotics of the critical twopoint function for the nearest-neighbor model with d 4 and for the spread-out model with d > 4 and L 1, without assuming reflection positivity.
Rights: "The original publication is available at"
資料タイプ: article (author version)
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 坂井 哲


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