Skip to main content
SpringerLink
Log in

Low-fugacity asymptotic expansion for classical lattice dipole gases

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

Abstract

We consider a classical dipole gas in the grand canonical ensemble. We prove that in dimensions greater than or equal to three, and for all temperatures, the free energy and the charges-dipoles correlation functions have an expansion in powers ofz, the fugacity of the system, which is asymptotic to all orders. We also give some information about the decay of correlations.

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. J. Bricmont, J. R. Fontaine, J. L. Lebowitz, and Th. Spencer, Lattice Systems with a Continuous Symmetry. I. Perturbation Theory for Unbounded Spins,Commun. Math. Phys. 78:281–302(1980).

    Google Scholar 

  2. J. Bricmont, J. R. Fontaine, J. L. Lebowitz, and Th. Spencer, Lattice Systems with a Continuous Symmetry. II. Decay of Correlation,Commun. Math. Phys. 78:363–371 (1981).

    Google Scholar 

  3. J. Bricmont, J. R. Fontaine, J. L. Lebowitz, E. H. Lieb, and Th. Spencer, Lattice Systems with a Continuous Symmetry III: Low Temperature Asymptotic Expansion for the Plane Rotator Model,Commun. Math. Phys. 78:545–566 (1981).

    Google Scholar 

  4. D. Brydyes,Commun. Math. Phys. 58:313 (1978).

    Google Scholar 

  5. J. Fröhlich and Y. M. Park,Commun. Math. Phys. 59:235 (1978).

    Google Scholar 

  6. J. Fröhlich and Th. Spencer, The Statistical Mechanics of Classical Coulomb and Dipole Gases,J. Stat. Phys. 24:617 (1981).

    Google Scholar 

  7. O. McBryan and Th. Spencer,Commun. Math. Phys. 53:99 (1977).

    Google Scholar 

  8. C. M. Newman, Normal Fluctuations and the F.K.G. Inequalities,Commun. Math. Phys. 74:119–128(1980).

    Google Scholar 

  9. Y. M. Park,Commun. Math. Phys. 70:161 (1979).

    Google Scholar 

  10. D. Ruelle,Statistical Mechanics (Benjamin, New York, 1969).

    Google Scholar 

  11. A. J. F. Siegert,Physica 26:30 (1960).

    Google Scholar 

  12. S. Weinberg,Phys. Rev. 118:838 (1960).

    Google Scholar 

  13. H. J. Brascamp and E. H. Lieb,J. Funct. Anal. 22:366 (1976).

    Google Scholar 

  14. G. Battle and L. Rosen,J. Stat. Phys. 22:128 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Rutgers Univercity, 08903, New Brunswick, New Jarsey

    J. R. Fontaine

Authors
  1. J. R. Fontaine
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

on leave from Institut de Physique Théorique Université de Louvian, Belgium. Supported by N.S.F. grant No. PHY-15920.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fontaine, J.R. Low-fugacity asymptotic expansion for classical lattice dipole gases. J Stat Phys 26, 767–782 (1981). https://doi.org/10.1007/BF01010938

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01010938

Key words

Search

Navigation