Skip to main content
SpringerLink
Log in

A simple proof of the GHS and further inequalities

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

Abstract

We formulate and prove a general set of correlation inequalities for spin — 1/2 Ising ferromagnets with pair interactions. One of these is the Griffiths-Hurst-Sherman inequality. The proof is obtained using Gaussian random variables.

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., Hurst, C.A., Sherman, S.: J. Math. Phys.11, 790 (1970)

    Google Scholar 

  2. Preston, C.J.: Commun. math. Phys.35, 253 (1974)

    Google Scholar 

  3. Lebowitz, J.L.: Commun. math. Phys.35, 87 (1974)

    Google Scholar 

  4. Monroe, J.L., Siegert, A.J.F.: J. Stat. Phys.10, 237 (1974)

    Google Scholar 

  5. Griffiths, R.B.: J. Math. Phys.8, 478, 484 (1967). Kelly, D.G., Sherman, S.: J. Math. Phys.9, 466 (1968)

    Google Scholar 

  6. Monroe, J.L.: J. Math. Phys.15, 998 (1974)

    Google Scholar 

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

    Google Scholar 

  8. Cramér, H.: Mathematical methods in statistics, p. 118. Princeton: Princeton University Press, N.J. 1951

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, Illinois, USA

    Richard S. Ellis

  2. Department of Physics, Northwestern University, Evanston, Illinois, USA

    James L. Monroe

Authors
  1. Richard S. Ellis
    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

Communicated by G. Gallavotti

Supported in part by National Science Foundation Grant GP-28576.

Supported by National Science Foundation Grant GP-36564-XI.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ellis, R.S., Monroe, J.L. A simple proof of the GHS and further inequalities. Commun.Math. Phys. 41, 33–38 (1975). https://doi.org/10.1007/BF01608545

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01608545

Keywords

Search

Navigation