Abstract
We prove that increasing function on a finite distributive lattice are positively correlated by positive measures satisfying a suitable convexity property. Applications to Ising ferromagnets in an arbitrary magnetic field and to the random cluster model are given.
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Fortuin, C.M., Kasteleyn, P.W. & Ginibre, J. Correlation inequalities on some partially ordered sets. Commun.Math. Phys. 22, 89–103 (1971). https://doi.org/10.1007/BF01651330
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DOI: https://doi.org/10.1007/BF01651330