Advertisement

Communications in Mathematical Physics

, Volume 35, Issue 4, pp 307–320 | Cite as

Strong cluster properties for classical systems with finite range interaction

  • M. Duneau
  • D. Iagolnitzer
  • B. Souillard
Article

Abstract

In a previous paper, “strong” decrease properties of the truncated correlation functions, taking into account the separation of all particles with respect to each other, have been presented and discussed.

In this paper, we prove these properties for finite range interactions in various situations, in particular
  1. i)

    at low activity for lattice and continuous systems,

     
  2. ii)

    at arbitrary activity and high temperature for lattice systems,

     
  3. iii)

    at ReH≠0, β arbitrary and atH=0 for appropriate temperatures in the case of ferromagnets.

     

We also give some general results, in particular an equivalence, on the links between analyticity and strong cluster properties of the truncated correlation functions.

Keywords

Neural Network Statistical Physic Correlation Function Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Duneau, M., Iagolnitzer, D., Souillard, B.: Commun. math. Phys.31, 191 (1973)Google Scholar
  2. 2.
    Lebowitz, J. L.: Commun. math. Phys.28, 313 (1972)Google Scholar
  3. 3.
    Gallavotti, G., Miracle-Sole, S.: Commun. math. Phys.12, 269 (1969)Google Scholar
  4. 4.
    Lebowitz, J. L., Penrose, O.: Commun. math. Phys.11, 99 (1968)Google Scholar
  5. 5.
    Ruelle, D.: Statistical mechanics, rigourous results. New York: Benjamin 1969Google Scholar
  6. 6.
    Yang, C. N., Lee, T. D.: Phys. Rev.87, 404 (1952)Google Scholar
  7. 7.
    Groeneveld, J.: Phys. Letters3, 50 (1962)Google Scholar
  8. 8.
    Ruelle, D.: Phys. Rev. Letters26, 303 (1971)Google Scholar
  9. 9.
    Lee, T. D., Yang, C. N.: Phys. Rev.87, 410 (1952)Google Scholar
  10. 10.
    Lieb, E. H., Ruelle, D.: J. Math. Phys.13, 781 (1972)Google Scholar
  11. 11.
    Ruelle, D.: Commun. math. Phys.31, 265 (1973)Google Scholar
  12. 12.
    Lebowitz, J. L., Penrose, O.: Decay of correlation, preprintGoogle Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • M. Duneau
    • 1
  • D. Iagolnitzer
    • 2
  • B. Souillard
    • 1
  1. 1.Centre de Physique Théorique de l'Ecole PolytechniqueParisFrance
  2. 2.Service de Physique ThéoriqueCentre d'Etudes Nucléaires de SaclayGif-sur-YvetteFrance

Personalised recommendations