Skip to main content
Log in

Perturbation theory for the triangular Heisenberg antiferromagnet with Ising-like anisotropy

  • Original Contributions
  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

It has been argued that the case of strong uniaxial anisotropy is especially favourable for the formation of a spin-liquid state in theS=1/2 triangular Heisenberg antiferromagnet [77]. We reconsider the old arguments using up-to-date numerical techniques, and extend the study to general values ofS. Recent progress in the understanding of this frustrated quantum spin system sheds light on the question why the original arguments in favour of an RVB state can not be conclusive. Our present results indicate that the tendency towards three-sublattice ordering is much stronger than it had been thought. However, the caseS=1/2 is still seen to be set apart from the casesS>1/2, and forS=1/2 the existence of true longrange order in the ground state remains debatable.

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.

Similar content being viewed by others

References

  1. Anderson, P.W.: Science235, 1196 (1987)

    Google Scholar 

  2. Toulouse, G.: Commun. Phys.2, 115 (1977)

    Google Scholar 

  3. Fazekas, P.: J. Phys. C13, L209 (1980)

    Google Scholar 

  4. Marshall, W.: Proc. R. Soc. Ser. A232, 48 (1955)

    Google Scholar 

  5. Anderson, P.W.: Mater. Res. Bull.8, 153 (1973)

    Google Scholar 

  6. Sütö, A., Fazekas, P.: Philos. Mag.35, 623 (1977)

    Google Scholar 

  7. Fazekas, P., Anderson, P.W.: Philos. Mag.30, 423 (1974)

    Google Scholar 

  8. Wannier, G.H.: Phys. Rev.79, 357 (1950)

    Google Scholar 

  9. Kleine, B., Müller-Hartmann, E., Frahm, K., Fazekas, P.: (to be published)

  10. Miyashita, S., Kawamura, H.: J. Phys. Soc. Jpn.54, 3385 (1985)

    Google Scholar 

  11. see also Miyashita, S.: Prog. Theor. Phys. Suppl.87, 112 (1986)

    Google Scholar 

  12. Ritchey, I., Coleman, P.: J. Phys.2, 9227 (1990)

    Google Scholar 

  13. Chubukov, A.V., Golosov, D.I.: J. Phys.3, 69 (1991)

    Google Scholar 

  14. Stephenson, J.: J. Math. Phys.5, 1009 (1964)

    Google Scholar 

  15. Takahashi, M.: J. Phys. C10, 1289 (1977)

    Google Scholar 

  16. For reviews, cf. Hirakawa, K., Kadowaki, H.: Physica B136, 335 (1986); Hirakawa, K.: Phase Trans.28, 33 (1990)

    Google Scholar 

  17. Kadowaki, H., Ubokoshi, K., Hirakawa, K.: J. Phys. Soc. Jpn.54, 363 (1985)

    Google Scholar 

  18. Kadowaki, H., Kikuchi, H., Ajiro, Y., J. Phys.2, 4485 (1990)

    Google Scholar 

  19. Hirakawa, K., Kadowaki, H., Ubukoshi, K.: J. Phys. Soc. Jpn.54, 3526 (1985)

    Google Scholar 

  20. Hirota, K., Nakazawa, Y., Ishikawa, M.: J. Phys.3, 4721 (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kleine, B., Fazekas, P. & Müller-Hartmann, E. Perturbation theory for the triangular Heisenberg antiferromagnet with Ising-like anisotropy. Z. Physik B - Condensed Matter 86, 405–410 (1992). https://doi.org/10.1007/BF01323734

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01323734

Keywords

Navigation