Advertisement

Journal of Statistical Physics

, Volume 9, Issue 4, pp 317–329 | Cite as

The correlation function in Wilson's theory of phase transitions: Above and below the transition

  • Daniel J. Amit
  • A. Shcherbakov
Articles

Abstract

The correlation function and the correlation length are discussed in the theoretical framework of the Wilson-Feynman diagram expansion for small ε=4−d. It is shown explicitly that to order ε2 the scaling relation γ= ν(2−η) is satisfied and that the correlation function is a homogeneous function ofk and ξ. The explicit form of the scaled correlation function is exhibited.

Key words

Correlation function ɛ-expansion ordered state phase transition 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. G. Wilson,Phys. Rev. Lett. 28:548 (1972).Google Scholar
  2. 2.
    E. Brezin, D. J. Wallace, and K. G. Wilson,Phys. Rev. Lett. 29:591 (1972).Google Scholar
  3. 3.
    E. Brezin, D. J. Wallace, and K. G. Wilson,Phys. Rev. B 7:232 (1973).Google Scholar
  4. 4.
    R. B. Griffiths,Phys. Rev. 158:176 (1967).Google Scholar
  5. 5.
    L. P. Kadanoff,Physics 2:263 (1966).Google Scholar
  6. 6.
    C. Di Castro,Lett. Nuovo Cimento 5:69 (1972), and private communication.Google Scholar
  7. 7.
    C. G. Callan Jr.,Phys. Rev. D 2:1541 (1970); K. Symanzik,Commun. Math. Phys. 18:227 (1970);23:49 (1971).Google Scholar
  8. 8.
    E. Brezin, J. C. Le Guillou, and J. Zinn-Justin, Saclay preprint DPh-T/72/100.Google Scholar
  9. 9.
    D. J. Amit and M. Zannetti,J. Stat. Phys. 7:31 (1973).Google Scholar
  10. 10.
    D. J. Amit,Physics Lett. 42A:299 (1972).Google Scholar
  11. 11.
    K. G. Wilson and J. B. Kogut,Phys. Reports (to be published).Google Scholar
  12. 12.
    E. Brezin, J. C. Le Guillou, and J. Zinn-Justin, Saclay preprint DPh-T/73/24.Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • Daniel J. Amit
    • 1
  • A. Shcherbakov
    • 2
  1. 1.Service de Physique ThéoriqueCentre d'Etudes Nucléaires de SaclayGif-sur-YvetteFrance
  2. 2.Racah Institute of PhysicsHebrew UniversityJerusalemIsrael

Personalised recommendations