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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク N-vector model ： ウィキペディア英語版 N-vector model The ''n''-vector model or O(''n'') model has been introduced by H. Eugene Stanley 〔H. E. Stanley, "Dependence of Critical Properties upon Dimensionality of Spins," Phys. Rev. Lett. 20, 589-592 (1968).〕 is one of the many highly simplified models in the branch of physics known as statistical mechanics. In the ''n''-vector model, ''n''-component, unit length, classical spins $\backslash mathbf\_i$ are placed on the vertices of a lattice. The Hamiltonian of the n-vector model is given by: :$H\; =\; -J\_\backslash mathbf\_i\; \backslash cdot\; \backslash mathbf\_j$ where the sum runs over all pairs of neighboring spins and $\backslash cdot$ denotes the standard Euclidean inner product. Special cases of the n-vector model are: :$n=0$ || The Self-Avoiding Walks (SAW) :$n=1$ || The Ising model :$n=2$ || The XY model :$n=3$ || The Heisenberg model :$n=4$ || Toy model for the Higgs sector of the Standard Model The general mathematical formalism used to describe and solve the ''n''-vector model and certain generalizations are developed in the article on the Potts model. ==References== () H. E. Stanley, "Dependence of Critical Properties upon Dimensionality of Spins," (Phys. Rev. Lett. 20, 589-592 (1968) ). This paper is the basis of many articles in field theory and is reproduced as Chapter 1 of Brèzin/Wadia () ''(The Large-N expansion in Quantum Field Theory and Statistical Physics )'' (World Scientific, Singapore, 1993). Also described extensively in the text Pathria RK ''(Statistical Mechanics: Second Edition )'' (Pergamon Press, Oxford, 1996). * P.G. de Gennes, Phys. Lett. A, 38, 339 (1972) noticed that the $n=0$ case corresponds to the SAW. * George Gaspari, Joseph Rudnick, Phys. Rev. B, 33, 3295 (1986) discuss the model in the limit of $n$ going to 0. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「N-vector model」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.