Kosterlitz-Thouless Transition and Mayer Expansion

  • Keiichi R. Ito
Part of the Progress in Physics book series (PMP, volume 11)

Summary

We discuss the Kosterlitz-Thouless transition in the 2D XY model by the Mayer expansion after transforming the model into a 2D Coulomb gas system by the duality transformation.

Keywords

Covariance Sine 

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References

  1. [1]
    V. Berezinskii, Sov.Phys. JETP 32 (1971) 493.Google Scholar
  2. [2]
    D.D. Brydgesand P. Federbush, J.Math.Phys. 19 (1978) 2064CrossRefGoogle Scholar
  3. D.D. Brydgesand P. Federbush, Comm. Math.Phys. 73 (1980) 197.CrossRefGoogle Scholar
  4. [3]
    J. Bricmont, J.R. Fontaine, J.L. Lebowitz, T. Spencer, and E. Lieb, Commun.Math.Phys. 78 (1980) 281, 363, 545.Google Scholar
  5. [4]
    L. Faddeev and L. Takhtajan, Integrability of Quantum 0(3) nonlinear a-Model, (LOMI Preprint, E-4–83).Google Scholar
  6. [5]
    J. Fröhlich and T. Spencer, Phys.Rev.Letters 46 (1981) 1006CrossRefGoogle Scholar
  7. J. Fröhlich and T. Spencer, Commun.Math.Phys. 81 (1981) 525.Google Scholar
  8. [6]
    J. Fröhlich and T. Spencer, Commun.Math.Phys. 83 (1982) 411.CrossRefGoogle Scholar
  9. [7]
    J.R. Fontaine, J. Statistical Phys. 26 (1981) 767.CrossRefGoogle Scholar
  10. [8]
    K. Gawedzki and A. Kupiainen, Ann.Phys. 147 (1983) 198.CrossRefGoogle Scholar
  11. [9]
    K. Gawedzki and A. Kupiainen, Commun.Math.Phys. 81 (1981) 191.Google Scholar
  12. [10]
    K.R. Ito, J. Statistical Phys. 29 (1982) 747.CrossRefGoogle Scholar
  13. [11]
    K.R. Ito, Study of the Kosterlitz-Thouless Transition by the Mayer Expansion, -Finiteness of the Perturbations -, (Bedford College Preprint (1983), to appear in Ann. Phys. (1984).)Google Scholar
  14. K.R. Ito, Phys.Letters 94A (1983) 339.Google Scholar
  15. [12]
    M. Lüscher and B. Berg, Commun.Math.Phys. 69 (1979) 57:Google Scholar
  16. Y. Iwasaki, Phys.Rev.Letters 47 (1981) 754.CrossRefGoogle Scholar
  17. [13]
    J. Jose, L. Kadanoff, S. Kirkpatrick and S. Nelson, Phys.Rev. B16 (1977) 1217.CrossRefGoogle Scholar
  18. [14]
    J. Kosterlitz and J. Thouless, J.Phys. C6 (1973) 1181: J. Kosterlitz, J.Phys. C7 (1974) 1047.Google Scholar
  19. [15]
    P. Kullish, Contribution to these proceedings.Google Scholar
  20. [16]
    McBryan and T. Spencer, Commun.Math.Phys. 53 (1977) 99.CrossRefGoogle Scholar
  21. [17]
    G. Mack and M. Göpfert, Commun.Math.Phys. 82 (1982) 545.CrossRefGoogle Scholar
  22. [18]
    A. Polyakov and P. Wiegman, Theory of Non-Abelian Goldstone Bosons, (Landau Institute Preprint, 1983 ).Google Scholar
  23. [19]
    D. Ruelle, Statistical Mechanics, Rigorous Results, Chap. 4 ( Benjamin, New York 1969 ).Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Keiichi R. Ito
    • 1
  1. 1.Department of MathematicsBedford College University of LondonLondonUK

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