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.
Similar content being viewed by others
References
Griffiths, R. B.: J. Math. Phys.8, 478, 484 (1967).
Kelly, D. G., Sherman, S.: J. Math. Phys.9, 466 (1968).
Sherman, S.: Commun. math. Phys.14, 1 (1969).
Ginibre, J.: Phys. Rev. Letters23, 828 (1969).
—— Commun. math. Phys.16, 310 (1970).
Harris, T. E.: Proc. Cambridge Phil. Soc.56, 13 (1960).
Kasteleyn, P. W., Fortuin, C. M.: J. Phys. Soc. Japan26 (Suppl.), 11 (1969).
Fortuin, C. M., Kasteleyn, P. W.: To be published.
Birkhoff, G.: Lattice theory. Am. Math. Soc., Providence (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01651330