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Journal of Statistical Physics

, Volume 38, Issue 5–6, pp 823–850 | Cite as

Two-body correlations and pair formation in the two-dimensional Coulomb gas

  • J. P. Hansen
  • P. Viot
Articles

Abstract

We investigate pair correlations in the two-dimensional Coulomb gas made up of two species of point ions carrying electric charges Z1e(>0) and Z2e(<0), and interaction by the logarithmic Coulomb potential. This system is known to be classically stable for couplingsΓ=e2/kBT<Tc=2/¦Z1Z2¦ (whereT is the temperature). Correlations between equally charged ions are shown to be greatly modified at short distances, in the rangeΓc/2<Γ<Γc, due to gradual ion “condensation.” The usual integral equations for the pair correlation functions admit no solutions in that range. Preliminary Monte Carlo simulations for the symmetric case (Z1=−Z2) reveal a striking “chemical” equilibrium between tightly bound ion pairs and free ions, which is reasonably well described by a simple Bjerrum model.

Key words

Two-dimensional Coulomb gas pair correlation functions integral equations ion pairing Monte Carlo simulations 

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References

  1. 1.
    B. Jancovici,Phys. Rev. Lett. 46:386 (1981).Google Scholar
  2. 2.
    J. M. Kosterlitz and D. J. Thouless,J. Phys. C 6:1181 (1973).Google Scholar
  3. 3.
    J. Fröhlich and T. Spencer,Phys. Rev. Lett. 46:1006 (1981).Google Scholar
  4. 4.
    S. T. Chui and J. D. Weeks,Phys. Rev. B 14:4978 (1976).Google Scholar
  5. 5.
    E. H. Lieb,Rev. Mod. Phys. 48:553 (1976).Google Scholar
  6. 6.
    E. H. Hauge and P. C. Hemmer,Phys. Norv. 5:209 (1971); see also D. Nicolaides,Phys. Lett. 103A:64 (1984).Google Scholar
  7. 7.
    J. Fröhlich,Commun. Math. Phys. 47:233 (1976).Google Scholar
  8. 8.
    C. Deutsch and M. Lavaud,Phys. Rev. A 9:2598 (1974).Google Scholar
  9. 9.
    J. P. Hansen and I. R. McDonald,Phys. Rev. A 23:2041 (1981); B. Bernu, J. P. Hansen, and R. Mazighi,Phys. Lett. 100A:28 (1984).Google Scholar
  10. 10.
    See, e.g., H. Minoo, M. M. Gombert, and C. Deutsch,Phys. Rev. A 23:924 (1981).Google Scholar
  11. 11.
    J. P. Hansen and P. Viot,Phys. Lett. 95A:155 (1983).Google Scholar
  12. 12.
    A. Salzberg and S. Prager,J. Chem. Phys. 38:2587 (1963); R. M. May,Phys. Lett. 25A:282 (1967).Google Scholar
  13. 13.
    F. H. Stillinger and R. Lovett,J. Chem. Phys. 49:1991 (1968).Google Scholar
  14. 14.
    D. J. Mitchell, D. A. Mc Quarrie, A. Szabo, and J. Groneveld,J. Stat. Phys. 17:15 (1977).Google Scholar
  15. 15.
    Ph. A. Martin and Ch. Gruber,J. Stat. Phys. 31:691 (1983).Google Scholar
  16. 16.
    L. Blum, C. Gruber, J. L. Lebowitz, and P. Martin,Phys. Rev. Lett. 48:1769 (1982).Google Scholar
  17. 17.
    See, e.g., M. Parrinello and M. P. Tosi,Riv. Nuovo Cimento 2(6):1 (1979).Google Scholar
  18. 18.
    G. S. Manning,J. Chem. Phys. 51:925 (1969).Google Scholar
  19. 19.
    B. Widom,J. Chem. Phys. 39:2808 (1963).Google Scholar
  20. 20.
    B. Jancovici,J. Stat. Phys. 17:357 (1977).Google Scholar
  21. 21.
    W. G. Hoover and J. C. Poirier,J. Chem. Phys. 37:1041 (1962).Google Scholar
  22. 22.
    K. S. Singwi, M. P. Tosi, R. H. Land, and A. Sjölander,Phys. Rev. 176:589 (1968).Google Scholar
  23. 23.
    R. Calinon, K. I. Golden, G. Kalman, and D. Merlini,Phys. Rev. A 20:329, 336 (1979).Google Scholar
  24. 24.
    M. Baus and J. P. Hansen,Phys. Rep. 59:1 (1980).Google Scholar
  25. 25.
    D. Henderson and L. Blum,J. Chem. Phys. 70:3149 (1979).Google Scholar
  26. 26.
    J. M. Caillol, D. Levesque, and J. J. Weiss,Mol. Phys. 44:733 (1981).Google Scholar
  27. 27.
    J. P. Hansen and D. Levesque,J. Phys. C 14:L603 (1981).Google Scholar
  28. 28.
    S. G. Brush, H. L. Sahlin, and E. Teller,J. Chem. Phys. 45:2102 (1966).Google Scholar
  29. 29.
    J. P. Valleau and S. G. Whittington, inStatistical Mechanics, part A, B. J. Berne, ed. (Plenum, New York, 1977).Google Scholar
  30. 30.
    N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. N. Teller, and E. Teller,J. Chem. Phys. 21:1087 (1953).Google Scholar
  31. 31.
    F. H. Stillinger and R. Lovett,J. Chem. Phys. 48:3858 (1968).Google Scholar
  32. 32.
    D. Cperley, G. V. Chester, and M. H. Kalos,Phys. Rev. B 16:3081 (1977).Google Scholar
  33. 33.
    C. Pangali, M. Rao, and B. J. Berne,Chem. Phys. Lett. 55:413 (1978).Google Scholar
  34. 34.
    M. Gillan, AERE Harwell report No. TP. 913 (1981).Google Scholar
  35. 35.
    B. Hafskjold and G. Stell, inStatistical Mechanics, E. Montroll and J. L. Lebowitz, eds. (North-Holland, Amsterdam, 1982).Google Scholar
  36. 36.
    N. Bjerrum,K. Dan. Vidensk. Selsk. 7:9 (1926).Google Scholar
  37. 37.
    J. S. Høye and K. Olaussen,Physica 104A:447 (1980); and107A:241 (1981).Google Scholar
  38. 38.
    P. Viot, Thèse de 3e Cycle, Université P. et M. Curie, Paris (1984).Google Scholar
  39. 39.
    J. L. Lebowitz and D. Mac Gowan, private communication.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • J. P. Hansen
    • 1
    • 2
  • P. Viot
    • 1
  1. 1.Laboratoire de Physique Théorique des Liquides, Equipe associée au CNRSUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.École Normale Supérieure de Saint-CloudSaint-CloudFrance

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