Skip to main content
SpringerLink
Log in

Inequalities for higher order Ising spins and for continuum fluids

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

Abstract

The recently derived Fortuin, Kasteleyn and Ginibre (FKG) inequalities for lattice gasses are investigated for higher order Ising spin systems and multi-component lattice gasses. Conditions are given for the validity of the FKG inequalities for higher order spin systems with Hamiltonians of the form used recently as models for various physical systems, e.g.He 3−He 4 mixtures. We also investigate various inequalities for binary lattice gases and show how these can be carried over to continuum systems.

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.

Similar content being viewed by others

References

  1. Griffiths. R. B.: Physica33, 689 (1967) and references given there.

    Google Scholar 

  2. Sivardieve, J., Blume, M.: Phys. Rev. B,5, 1126 (1972).

    Google Scholar 

  3. Bell, G. M., Lavis, D. A.: Phil. Mag.11, 937 (1965) and references given there.

    Google Scholar 

  4. Wheeler, J. C., Widom, B.: J. Chem. Phys.52, 5334 (1970), and references given there.

    Google Scholar 

  5. Helfand, E., Stillinger, F. H.: J. Chem. Phys.49, 1232 (1968).

    Google Scholar 

  6. Blume, M., Emery, V. J., Griffiths, R. B.: Phys. Rev. A4, 1071 (1971).

    Google Scholar 

  7. Griffiths, R. B.: J. Math. Phys.10, 1559 (1969).

    Google Scholar 

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

    Google Scholar 

  9. Kelly, D., Sherman, S.: J. Math. Phys.10, 1559 (1969).

    Google Scholar 

  10. Fortuin, C. M., Kasteleyn, P. W., Ginibre, J.: Commun. math. Phys.22, 89 (1971).

    Google Scholar 

  11. Lebowitz, J. L., Gallavotti, G.: J. Math. Phys.12, 1129 (1971).

    Google Scholar 

  12. Widom, B., Rowlinson, J. S.: J. Chem. Phys.52, 1670 (1970).

    Google Scholar 

  13. Ruelle, D.: Phys. Rev. Letters27, 1040 (1971).

    Google Scholar 

  14. Lebowitz, J. L., Lieb, E.: Phys. Letters39 A, 98 (1972).

    Google Scholar 

  15. Ruelle, D.: Statistical mechanics. New York: Benjamin 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belfer Graduate School of Science, Yeshiva University, New York, N.Y., USA

    Joel L. Lebowitz

  2. Dept. of Physics, Columbia University, New York, N.Y., USA

    James L. Monroe

Authors
  1. Joel L. Lebowitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. James L. Monroe
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported in part by U.S.A.F.O.S.R. # F 44620-71-C-0013.

N.S.F. Graduate Trainee.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lebowitz, J.L., Monroe, J.L. Inequalities for higher order Ising spins and for continuum fluids. Commun.Math. Phys. 28, 301–311 (1972). https://doi.org/10.1007/BF01645631

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01645631

Keywords

Search

Navigation