Skip to main content
SpringerLink
Log in

Mean field bound and GHS inequality

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

A new proof of the mean field bounds for magnetizations is presented. It applies to any single-component spin system which allows GHS inequality, and to anN-vector model forN ⩾ 3, and to anN-solid sphere model for all values ofN, provided that the interactions are ferromagnetic and translation invariant.

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. M. Aizenman,Commun. Math. Phys. 86:1 (1982).

    Google Scholar 

  2. J. Fröhlich, R. Israel, E. H. Lieb, and B. Simon,Commun. Math. Phys. 62:1 (1978).

    Google Scholar 

  3. J. Glimm and A. Jaffe,Quantum Physics—A Functional Integral Point of View (Springer, New York, 1981).

    Google Scholar 

  4. C. J. Thompson,Commun. Math. Phys. 24:61 (1971).

    Google Scholar 

  5. P. A. Pearce,J. Stat. Phys. 25:309 (1981).

    Google Scholar 

  6. A. D. Sokal,J. Stat. Phys. 28:431 (1982).

    Google Scholar 

  7. D. Ruelle,Statistical Mechanics-Rigorous Results (Benjamin, New York, 1969).

    Google Scholar 

  8. R. B. Griffiths, inStatistical Mechanics and Quantum Field Theory: 1970 Les Houches, C. DeWitt and R. Stora, eds. (Gordon & Breach, New York, 1971).

    Google Scholar 

  9. J. Fröhlich, B. Simon, and T. Spencer,Commun. Math. Phys. 50:79 (1976).

    Google Scholar 

  10. R. B. Griffiths, C. A. Hurst, and S. Sherman,J. Math. Phys. 11:790 (1970).

    Google Scholar 

  11. R. S. Ellis, J. L. Monroe, and C. M. Newman,Commun. Math. Phys. 46:167 (1976).

    Google Scholar 

  12. G. S. Sylvester,J. Stat. Phys. 15:327 (1976).

    Google Scholar 

  13. A. D. Sokal,J. Stat. Phys. 25:25 (1981).

    Google Scholar 

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

    Google Scholar 

  15. J. L. Monroe and P. A. Pearce,J. Stat. Phys. 21:615 (1979).

    Google Scholar 

  16. B. Simon,J. Stat. Phys. 22:491 (1980).

    Google Scholar 

  17. C. M. Newman, Shock Waves and Mean Field Bounds (announcement of results, University of Arizona, 1981).

  18. C. M. Newman, Talk at 46th Statistical Mechanics Meeting (Rutgers, New Jersey, 1981); seeJ. Stat. Phys. 27:836 (1982).

    Google Scholar 

  19. C. M. Newman, Talk at Functional Integral Method Workshop (Santa Barbara, California, 1982).

    Google Scholar 

  20. J. Slawny,J. Stat. Phys. 32:375 (1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, 113, Tokyo, Japan

    Hal Tasaki

  2. Institute of Physics, College of General Education, University of Tokyo, Komaba, Meguroku, 153, Tokyo, Japan

    Takashi Hara

Authors
  1. Hal Tasaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takashi Hara
    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

Tasaki, H., Hara, T. Mean field bound and GHS inequality. J Stat Phys 35, 99–107 (1984). https://doi.org/10.1007/BF01017367

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01017367

Key words

Search

Navigation