Correlation inequalities and the decay of correlations in ferromagnets

摘要: We prove a variety of new correlation inequalities which bound intermediate distance correlations from below by long correlations. Typical is the following holds for spin 1/2 nearest neighbor Ising ferromagnets: $$\langle S_\alpha S_\gamma \rangle \leqq \sum\limits_{\delta \in B} {\langle S_\delta } \langle \rangle$$ whereB any subset lattice whose removal divides into pieces with α,γ in distinct components. describe various applications, e.g. above inequality implies critical exponent η<1.