Skip to main content
SpringerLink
Log in

Correlation inequalities on some partially ordered sets

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Griffiths, R. B.: J. Math. Phys.8, 478, 484 (1967).

    Google Scholar 

  2. Kelly, D. G., Sherman, S.: J. Math. Phys.9, 466 (1968).

    Google Scholar 

  3. Sherman, S.: Commun. math. Phys.14, 1 (1969).

    Google Scholar 

  4. Ginibre, J.: Phys. Rev. Letters23, 828 (1969).

    Google Scholar 

  5. —— Commun. math. Phys.16, 310 (1970).

    Google Scholar 

  6. Harris, T. E.: Proc. Cambridge Phil. Soc.56, 13 (1960).

    Google Scholar 

  7. Kasteleyn, P. W., Fortuin, C. M.: J. Phys. Soc. Japan26 (Suppl.), 11 (1969).

    Google Scholar 

  8. Fortuin, C. M., Kasteleyn, P. W.: To be published.

  9. Birkhoff, G.: Lattice theory. Am. Math. Soc., Providence (1967).

Download references

Author information

Authors and Affiliations

  1. Instituut-Lorentz, Rijksuniversiteit te Leiden, Leiden, Nederland

    C. M. Fortuin & P. W. Kasteleyn

  2. Laboratoire de Physique Théorique et Hautes Energies, Université de Paris-Sud (Laboratorie associé au Centre National de la Recherche Scientifique), Orsay, France

    J. Ginibre

Authors
  1. C. M. Fortuin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. W. Kasteleyn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Ginibre
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01651330

Keywords

Search

Navigation