Skip to main content
Log in

Exact results for the two-dimensional, two-component plasma atΓ=2 in doubly periodic boundary conditions

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The two-dimensional, two-component plasma is considered in doubly periodic boundary conditions with the positive and negative charges confined to separate interlacing rectangular lattices. It is shown that at the special couplingΓ=2, on a lattice of 2M 1×2M 2 sites, the grand partition function can be written as a double integral over a product of determinants of dimension 2M 2×2M 2. On the basis of a conjecture regarding the zero distribution of the grand partition function, the large-M 2 behavior of the determinant is given and the pressure evaluated exactly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. M. Kosterlitz and D. J. Thouless,J. Phys. C 6:1181 (1973).

    Google Scholar 

  2. D. R. Nelson, inPhase Transitions and Critical Phenomena, Vol. 7, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York).

  3. P. Minnhagen,Rev. Mod. Phys. 59:1001 (1987).

    Google Scholar 

  4. J. Villain, inOrdering in Strongly Fluctuating Condensed Matter Systems, T. Riste, ed. (Plenum, New York, 1980), p. 221.

    Google Scholar 

  5. B. Neinhuis, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York).

  6. J. Zittartz,Z. Phys. B 23:55 (1976).

    Google Scholar 

  7. C. N. Yang and T. D. Lee,Phys. Rev. 87:404 (1952).

    Google Scholar 

  8. C. Gallavoti and F. Nicoló,J. Stat. Phys. 39:133 (1985).

    Google Scholar 

  9. P. J. Forrester,J. Stat. Phys., to appear.

  10. P. J. Forrester,J. Stat. Phys. 51:457 (1988).

    Google Scholar 

  11. M. Gaudin,J. Phys. (Paris)46:1027 (1985).

    Google Scholar 

  12. J. W. Perram and S. W. de Leeuw,Physica 109A:237 (1981).

    Google Scholar 

  13. M. L. Glasser,J. Math. Phys. 15:188 (1974).

    Google Scholar 

  14. J. D. Fay,Lecture Notes in Mathematics, No. 352 (1973).

  15. P. J. Forrester,SIAM J. Math. Anal. 21:270 (1990).

    Google Scholar 

  16. F. Cornu and B. Jancovici,J. Stat. Phys. 49:33 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Forrester, P.J. Exact results for the two-dimensional, two-component plasma atΓ=2 in doubly periodic boundary conditions. J Stat Phys 61, 1141–1160 (1990). https://doi.org/10.1007/BF01014369

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01014369

Key words

Navigation