Journal of Statistical Physics

, Volume 43, Issue 1–2, pp 17–32 | Cite as

Phase transitions in two-dimensional uniformly frustratedXY models. II. General scheme

  • S. E. Korshunov


For two-dimensional uniformly frustratedXY models the group of symmetry spontaneously broken in the ground state is a cross product of the group of two-dimensional rotations by some discrete group of finite order. Different possibilities of phase transitions in such systems are investigated. The transition to the Coulomb gas with noninteger charges is widely used when analyzing the properties of relevant topological excitations. The number of these excitations includes not only domain walls and traditional (integer) vortices, but also vortices with a fractional number of circulation quanta which are to be localized at bends and intersections of domain walls. The types of possible phase transitions prove to be dependent on their relative sequence: in the case the vanishing of domain wall free energy occurs earlier (at increasing temperature) than the dissociation of pairs of ordinary vortices, the second phase transition is to be associated with dissociation of pairs of fractional vortices. The general statements are illustrated with a number of examples.

Key words

Two-dimensional systems phase transitions frustratedXY models topological excitations fractional vortices Josephson junctions superfluid3He-A thin films 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. E. Korshunov and G. V. Uimin, previous paper of this issue.Google Scholar
  2. 2.
    S. Teitel and C. Jayaprakash,Phys. Rev. B27:598 (1983).Google Scholar
  3. 3.
    S. Teitel and C. Jayaprakash,Phys. Rev. Lett. 51:1999 (1983).Google Scholar
  4. 4.
    W. Y. Shih and D. Stroud,Phys. Rev. B28:6575 (1983).Google Scholar
  5. 5.
    W. Y. Shih and D. Stroud,Phys. Rev. B30:6774 (1984);B32:158 (1985).Google Scholar
  6. 6.
    V. L. Berezinskii, Thesis (L. D. Landau Institute for Theoretical Physics, Moscow, 1971, unpublished).Google Scholar
  7. 7.
    J. Villain,J. Physique 36:581 (1975).Google Scholar
  8. 8.
    E. Fradkin, B. A. Huberman, and S. H. Shenker,Phys. Rev. B18:4789 (1978).Google Scholar
  9. 9.
    J. Villain,J. Phys. C 10:1717 (1977).Google Scholar
  10. 10.
    J. Villain,J. Phys. C 10:4793 (1977).Google Scholar
  11. 11.
    Z. Tešanovič,Phys. Lett. 100A:158 (1984).Google Scholar
  12. 12.
    G. E. Volovik and M. M. Salomaa,Zh. Eksp. Teor. Fiz. 87:1656 (1985);Phys. Rev. Lett. 55:1184 (1985).Google Scholar
  13. 13.
    S. Miyashita and J. Shiba,J. Phys. Soc. Jap. 53:1145 (1984).Google Scholar
  14. 14.
    F. Y. Wu and K. Y. Lin,J. Phys. C 7:L181 (1974).Google Scholar
  15. 15.
    H. J. F. Knops,J. Phys. A 8:1508 (1975).Google Scholar
  16. 16.
    S. E. Ashley,J. Phys. A 11:2015 (1978).Google Scholar
  17. 17.
    R. J. Baxter,J. Phys. A 13:L61 (1980).Google Scholar
  18. 18.
    J. M. Kosterlitz and D. J. Thouless,J. Phys. C 6:1181 (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • S. E. Korshunov
    • 1
  1. 1.L. D. Landau Institute for Theoretical PhysicsAcademy of Sciences of the USSRMoscowUSSR

Personalised recommendations