Skip to main content
SpringerLink
Log in

Gaussian bounds for correlations in lattice spin systems

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

Abstract

In quite generalN-component ferromagnetic spin systems, it is proved that an arbitrary correlation function is bounded by the corresponding correlation function of a Gaussian model. The bound is useful for the analysis of high-temperature behavior of the system. Similar bounds for truncated correlation functions are also obtained for a class of single-component spin 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.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. H. Berlin and M. Kac,Phys. Rev. 86:821 (1952).

    Google Scholar 

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

    Google Scholar 

  3. D. C. Brydges, J. Fröhlich, and A. D. Sokal,Commun. Math. Phys. 91:141 (1983).

    Google Scholar 

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

    Google Scholar 

  5. T. Hara, T. Hattori, and H. Tasaki, submitted toJ. Math. Phys.

  6. D. Ruelle,Statistical Mechanics—Rigorous Results (Benjamin, New York, 1969).

    Google Scholar 

  7. J. Glimm and A. Jaffe,Quantum Physics—A Functional Integral Ppoint of View (Gordon & Breach, New York, 1971).

    Google Scholar 

  8. M. E. Fisher,Phys. Rev. 162:480 (1967).

    Google Scholar 

  9. J. L. Lebowitz, inMathematical Problems in Theoretical Physics (Kyoto 1975) Lecture Notes in Physics #39, H. Araki ed. (Springer Verlag, Berlin, 1975), p. 370.

    Google Scholar 

  10. D. Weingarten,Phys. Lett. 90B:280 (1980).

    Google Scholar 

  11. T. Eguchi and H. Kawai,Phys. Lett. 110B:143 (1982); and114B:247 (1982).

    Google Scholar 

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

    Google Scholar 

  13. C. M. Newman, unpublished; see Ref. 16.

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

    Google Scholar 

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

    Google Scholar 

  16. H. Tasaki and T. Hara,J. Stat. Phys. 35:99 (1984).

    Google Scholar 

  17. M. Aizenman and B. Simon,Commun. Math. Phys. 77:137 (1980).

    Google Scholar 

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

    Google Scholar 

  19. S. T. Levin,Commun. Math. Phys. 78:65 (1980).

    Google Scholar 

  20. D. Brydges, J. Fröhlich, and T. Spencer,Commun. Math. Phys. 83:123 (1982).

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  25. B. Siu, Caltech preprint (CALT-68-1106), and thesis (Caltech, 1984).

  26. H. Tasaki and T. Hara, A Model of Random Surfaces including Arbitrary Surfaces, submitted toPhys. Lett. A (1984).

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

Authors
  1. Hal Tasaki
    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. Gaussian bounds for correlations in lattice spin systems. J Stat Phys 38, 873–890 (1985). https://doi.org/10.1007/BF01010421

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01010421

Key words

Search

Navigation