Journal of Statistical Physics

, Volume 43, Issue 1–2, pp 1–16 | Cite as

Phase transitions in two-dimensional uniformly frustratedXY models. I. Antiferromagnetic model on a triangular lattice

  • S. E. Korshunov
  • G. V. Uimin


A most popular model in the family of two-dimensional uniformly-frustratedXY models is the antiferromagnetic model on a triangular lattice [AFXY(t) model]. Its ground state is both continuously and twofold discretely degenerated. Different phase transitions possible in such systems are investigated. Relevant topological excitations are analyzed and a new class of such (vortices with a fractional number of circulation quanta) is discovered. Their role in determining the properties of the system proves itself essential. The characteristics of phase transitions related to breaking of discrete and continuous symmetries change. The phase diagram of the “generalized” AFXY(t) model is constructed. The results obtained are rederived in the representation of the Coulomb gas with half-integer charges, equivalent to the AFXY(t) model with the Berezinskii-Villain interaction.

Key words

Two-dimensional systems phase transitions frustratedXY models antiferromagneticXY model topological excitations fractional vortices Coulomb gas Josephson junctions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Peierls,Helv. Phys. Acta VIII, Suppl. 2:81 (193).Google Scholar
  2. 2.
    L. D. Landau,Zh. Eksp. Teor. Fiz. 7:627 (1937).Google Scholar
  3. 3.
    N. Mermin and H. Wagner,Phys. Rev. Lett. 17:1133 (1966).Google Scholar
  4. 4.
    P. C. Hohenberg,Phys. Rev. 158:383 (1967).Google Scholar
  5. 5.
    V. L. Berezinskii,Zh. Eksp. Teor. Fiz. 59:907 (1970); [Sov. Phys.—JETP 32:493 (1971)].Google Scholar
  6. 6.
    V. L. Berezinskii,Zh. Eksp. Teor. Fiz. 61:1144 (1971); [Sov. Phys.—JETP 34:610 (1972)].Google Scholar
  7. 7.
    V. L. Berezinskii, Thesis (L. D. Landau Institute for Theoretical Physics, Moscow, 1971, unpublished).Google Scholar
  8. 8.
    J. M. Kosterlitz and J. D. Thouless,J. Phys. C 6:1186 (1973).Google Scholar
  9. 9.
    J. M. Kosterlitz,J. Phys. C 7:1046 (1974).Google Scholar
  10. 10.
    S. Miyashita and J. Shiba,J. Phys. Soc. Jap. 53:1145 (1984).Google Scholar
  11. 11.
    D. H. Lee, R. G. Caflisch, J. D. Joannopoulos, and F. Y. Wu,Phys. Rev. B29:2680 (1984);B33:450 (1986).Google Scholar
  12. 12.
    D. H. Lee, J. D. Joannopoulos, J. W. Negele, and D. P. Landau,Phys. Rev. Lett. 52:433 (1984).Google Scholar
  13. 13.
    Vik. S. Dotsenko and G. V. Uimin,Pis'ma Zh. Eksp. Teor. Fiz. 40:236 (1984);J. Phys. C 18:5019 (1985).Google Scholar
  14. 14.
    W. Y. Shih and D. Stroud,Phys. Rev. B30:6774 (1984);B32:158 (1985).Google Scholar
  15. 15.
    P. W. Stephens, P. A. Heiney, R. J. Birgeneau, P. M. Horn, J. Stoltenberg, and O. E. Viches,Phys. Rev. Lett. 45:1959 (1980).Google Scholar
  16. 16.
    H. Suematsu, K. Ohmatsu, K. Sugiyama, T. Sakakibara, M. Motokawa, and M. Date,Solid State Commun. 40:241 (1981).Google Scholar
  17. 17.
    R. F. Voss and R. A. Webb,Phys. Rev. B25:3446 (1982).Google Scholar
  18. 18.
    R. A. Webb, R. F. Voss, G. Grinstein, and P. M. Horn,Phys. Rev. Lett. 51:690 (1983).Google Scholar
  19. 19.
    M. Tinkham, D. W. Abrahams, and C. J. Lobb,Phys. Rev. B28:6578 (1983).Google Scholar
  20. 20.
    D. Kimhi, F. Leyvraz, and D. Arioza,Phys. Rev. B29:1487 (1984).Google Scholar
  21. 21.
    S. Teitel and C. Jayaprakash,Phys. Rev. B27:598 (1983).Google Scholar
  22. 22.
    S. Teitel and C. Jayaprakash,Phys. Rev. Lett. 51:1999 (1983).Google Scholar
  23. 23.
    W. Y. Shih and D. Stroud,Phys. Rev. B28:6575 (1983).Google Scholar
  24. 24.
    S. E. Korshunov, Next paper of this issue.Google Scholar
  25. 25.
    S. E. Korshunov,Pis'ma Zh. Eksp. Teor. Fiz. 41:525 (1985):JETP Lett. 41:641 (1985).Google Scholar
  26. 26.
    S. E. Korshunov,Pis'ma Zh. Eksp. Teor. Fiz. 41:216 (1985);JETP Lett. 41:263 (1985).Google Scholar
  27. 27.
    A. B. Zamolodchikov,Zh. Eksp. Teor. Fiz. 79:341 (1978); Vl. S. Dotsenko,Zh. Eksp. Teor. Fiz. 75:1083 (1978).Google Scholar
  28. 28.
    B. Nienhuis, R. K. Riedel, and M. Shick,Phys. Rev. B27:5625 (1983).Google Scholar
  29. 29.
    J. Villain,J. Physique 36:581 (1975).Google Scholar
  30. 30.
    J. V. José, L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson,Phys. Rev. B16:1217 (1977).Google Scholar
  31. 31.
    J. Villain,J. Phys. C 10:4793 (1977).Google Scholar
  32. 32.
    E. Fradkin, B. A. Huberman, and S. H. Shenker,Phys. Rev. B18:4789 (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

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

Personalised recommendations