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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 Griffiths inequality ： ウィキペディア英語版 Griffiths inequality In statistical mechanics, the Griffiths inequality, sometimes also called Griffiths–Kelly–Sherman inequality or GKS inequality, named after Robert B. Griffiths, is a correlation inequality for ferromagnetic spin systems. Informally, it says that in ferromagnetic spin systems, if the 'a-priori distribution' of the spin is invariant under spin flipping, the correlation of any monomial of the spins is non-negative; and the two point correlation of two monomial of the spins is non-negative. The inequality was proved by Griffiths for Ising ferromagnets with two-body interactions, then generalised by Kelly and Sherman to interactions involving an arbitrary number of spins, and then by Griffiths to systems with arbitrary spins. A more general formulation was given by Ginibre, and is now called the Ginibre inequality. ==Definitions== Let $\backslash textstyle\; \backslash sigma=\backslash \_$ be a configuration of (continuous or discrete) spins on a lattice ''Λ''. If ''A'' ⊂ ''Λ'' is a list of lattice sites, possibly with duplicates, let $\backslash textstyle\; \backslash sigma\_A\; =\; \backslash prod\_\; \backslash sigma\_j$ be the product of the spins in ''A''. Assign an ''a-priori'' measure ''dμ(σ)'' on the spins; let ''H'' be an energy functional of the form :$H(\backslash sigma)=-\backslash sum\_\; J\_A\; \backslash sigma\_A\; ~,$ where the sum is over lists of sites ''A'', and let :$Z=\backslash int\; d\backslash mu(\backslash sigma)\; e^$ be the partition function. As usual, :$\backslash langle\; \backslash cdot\; \backslash rangle\; =\; \backslash frac\; \backslash sum\_\backslash sigma\; \backslash cdot(\backslash sigma)\; e^$ stands for the ensemble average. The system is called ''ferromagnetic'' if, for any list of sites ''A'', ''JA ≥ 0''. The system is called ''invariant under spin flipping'' if, for any ''j'' in ''Λ'', the measure ''μ'' is preserved under the sign flipping map ''σ → τ'', where :$\backslash tau\_k\; =\; \backslash begin$ \sigma_k, &k\neq j, \\ - \sigma_k, &k = j. \end 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「Griffiths inequality」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.