Communications in Mathematical Physics

, Volume 22, Issue 2, pp 89–103 | Cite as

Correlation inequalities on some partially ordered sets

  • C. M. Fortuin
  • P. W. Kasteleyn
  • J. Ginibre


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.


Magnetic Field Neural Network Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Griffiths, R. B.: J. Math. Phys.8, 478, 484 (1967).Google Scholar
  2. 2.
    Kelly, D. G., Sherman, S.: J. Math. Phys.9, 466 (1968).Google Scholar
  3. 3.
    Sherman, S.: Commun. math. Phys.14, 1 (1969).Google Scholar
  4. 4.
    Ginibre, J.: Phys. Rev. Letters23, 828 (1969).Google Scholar
  5. 5.
    —— Commun. math. Phys.16, 310 (1970).Google Scholar
  6. 6.
    Harris, T. E.: Proc. Cambridge Phil. Soc.56, 13 (1960).Google Scholar
  7. 7.
    Kasteleyn, P. W., Fortuin, C. M.: J. Phys. Soc. Japan26 (Suppl.), 11 (1969).Google Scholar
  8. 8.
    Fortuin, C. M., Kasteleyn, P. W.: To be published.Google Scholar
  9. 9.
    Birkhoff, G.: Lattice theory. Am. Math. Soc., Providence (1967).Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • C. M. Fortuin
    • 1
  • P. W. Kasteleyn
    • 1
  • J. Ginibre
    • 2
  1. 1.Instituut-Lorentz, Rijksuniversiteit te LeidenLeidenNederland
  2. 2.Laboratoire de Physique Théorique et Hautes EnergiesUniversité de Paris-Sud (Laboratorie associé au Centre National de la Recherche Scientifique)OrsayFrance

Personalised recommendations