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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 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 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 : where the sum is over lists of sites ''A'', and let : be the partition function. As usual, : 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 : 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
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