Abstract
We investigate pair correlations in the two-dimensional Coulomb gas made up of two species of point ions carrying electric charges Z1 e(>0) and Z2 e(<0), and interaction by the logarithmic Coulomb potential. This system is known to be classically stable for couplingsΓ=e 2/k BT<Tc=2/¦Z1Z2¦ (whereT is the temperature). Correlations between equally charged ions are shown to be greatly modified at short distances, in the rangeΓ c/2<Γ<Γ c, 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Jancovici,Phys. Rev. Lett. 46:386 (1981).
J. M. Kosterlitz and D. J. Thouless,J. Phys. C 6:1181 (1973).
J. Fröhlich and T. Spencer,Phys. Rev. Lett. 46:1006 (1981).
S. T. Chui and J. D. Weeks,Phys. Rev. B 14:4978 (1976).
E. H. Lieb,Rev. Mod. Phys. 48:553 (1976).
E. H. Hauge and P. C. Hemmer,Phys. Norv. 5:209 (1971); see also D. Nicolaides,Phys. Lett. 103A:64 (1984).
J. Fröhlich,Commun. Math. Phys. 47:233 (1976).
C. Deutsch and M. Lavaud,Phys. Rev. A 9:2598 (1974).
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).
See, e.g., H. Minoo, M. M. Gombert, and C. Deutsch,Phys. Rev. A 23:924 (1981).
J. P. Hansen and P. Viot,Phys. Lett. 95A:155 (1983).
A. Salzberg and S. Prager,J. Chem. Phys. 38:2587 (1963); R. M. May,Phys. Lett. 25A:282 (1967).
F. H. Stillinger and R. Lovett,J. Chem. Phys. 49:1991 (1968).
D. J. Mitchell, D. A. Mc Quarrie, A. Szabo, and J. Groneveld,J. Stat. Phys. 17:15 (1977).
Ph. A. Martin and Ch. Gruber,J. Stat. Phys. 31:691 (1983).
L. Blum, C. Gruber, J. L. Lebowitz, and P. Martin,Phys. Rev. Lett. 48:1769 (1982).
See, e.g., M. Parrinello and M. P. Tosi,Riv. Nuovo Cimento 2(6):1 (1979).
G. S. Manning,J. Chem. Phys. 51:925 (1969).
B. Widom,J. Chem. Phys. 39:2808 (1963).
B. Jancovici,J. Stat. Phys. 17:357 (1977).
W. G. Hoover and J. C. Poirier,J. Chem. Phys. 37:1041 (1962).
K. S. Singwi, M. P. Tosi, R. H. Land, and A. Sjölander,Phys. Rev. 176:589 (1968).
R. Calinon, K. I. Golden, G. Kalman, and D. Merlini,Phys. Rev. A 20:329, 336 (1979).
M. Baus and J. P. Hansen,Phys. Rep. 59:1 (1980).
D. Henderson and L. Blum,J. Chem. Phys. 70:3149 (1979).
J. M. Caillol, D. Levesque, and J. J. Weiss,Mol. Phys. 44:733 (1981).
J. P. Hansen and D. Levesque,J. Phys. C 14:L603 (1981).
S. G. Brush, H. L. Sahlin, and E. Teller,J. Chem. Phys. 45:2102 (1966).
J. P. Valleau and S. G. Whittington, inStatistical Mechanics, part A, B. J. Berne, ed. (Plenum, New York, 1977).
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. N. Teller, and E. Teller,J. Chem. Phys. 21:1087 (1953).
F. H. Stillinger and R. Lovett,J. Chem. Phys. 48:3858 (1968).
D. Cperley, G. V. Chester, and M. H. Kalos,Phys. Rev. B 16:3081 (1977).
C. Pangali, M. Rao, and B. J. Berne,Chem. Phys. Lett. 55:413 (1978).
M. Gillan, AERE Harwell report No. TP. 913 (1981).
B. Hafskjold and G. Stell, inStatistical Mechanics, E. Montroll and J. L. Lebowitz, eds. (North-Holland, Amsterdam, 1982).
N. Bjerrum,K. Dan. Vidensk. Selsk. 7:9 (1926).
J. S. Høye and K. Olaussen,Physica 104A:447 (1980); and107A:241 (1981).
P. Viot, Thèse de 3e Cycle, Université P. et M. Curie, Paris (1984).
J. L. Lebowitz and D. Mac Gowan, private communication.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hansen, J.P., Viot, P. Two-body correlations and pair formation in the two-dimensional Coulomb gas. J Stat Phys 38, 823–850 (1985). https://doi.org/10.1007/BF01010417
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01010417