Skip to main content
SpringerLink
Log in

Phase transitions in anisotropic classical Heisenberg ferromagnets

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

The method of Peierls is used to prove the existence of a spontaneous magnetization for a spin system with nearest-neighbor interactions and Hamiltonian\(H = - J \sum\limits_{\left\langle {ij} \right\rangle } { [S_i^z S_j^z + \alpha (S_i^x S_j^x + S_i^y S_i^y )], S_i } \) a (classical) unit vector at thei'th site, with |α|<0.0298 and 0.0198 for a square lattice and simple cubic lattice, respectively.

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

Access this article

Log in via an institution

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. Peierls, R.: Proc. Cambridge Phil. Soc.32, 477 (1936).

    Google Scholar 

  2. Dobrushin, R. L.: Teor. Veroyat. Ee Primen.10, 209 (1965).

    Google Scholar 

  3. Griffiths, R. B.: Phys. Rev.136, A437 (1964).

    Google Scholar 

  4. —— In: Phase transitions and critical phenomena, C. Domb and M.S. Green, eds, Vol. I. London: Academic Press 1972.

    Google Scholar 

  5. Ruelle, D.: Phys. Rev. Letters27, 1040 (1971).

    Google Scholar 

  6. Ginibre, J.: Commun. math. Phys.14, 205 (1969).

    Google Scholar 

  7. Fisher, M. E.: J. Appl. Phys.38, 981 (1967).

    Google Scholar 

  8. Mermin, N. D., Wagner, H.: Phys. Rev. Letters17, 1133 (1966).

    Google Scholar 

  9. Millard, K., Leff, H. S.: J. Math. Phys.12, 1000 (1971).

    Google Scholar 

  10. Griffiths, R. B.: J. Math. Phys.10, 1559 (1969).

    Google Scholar 

  11. Tebble, R. S.: Magnetic domains, p. 34. London: Methuen & Co., Ltd. 1969.

    Google Scholar 

  12. Döring, W.: In: Flügge, S. (Ed.): Handbuch der Physik, Vol. 18/2, p. 341. Berlin-Heidelberg-New York: Springer 1966.

    Google Scholar 

  13. Robinson, D. W.: Commun. math. Phys.14, 195 (1969).

    Google Scholar 

Download references

Author information

Author notes

  1. Alfred B. Bortz

    Present address: Bowling Green State University, Firelands Campus, 44839, Huron, Ohio, USA

Authors and Affiliations

  1. Department of Physics, Carnegie-Mellon University, Pittsburgh, Pennsylvania, USA

    Alfred B. Bortz & Robert B. Griffiths

Authors
  1. Alfred B. Bortz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert B. Griffiths
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by the National Science Foundation Grant No. GP 11454.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bortz, A.B., Griffiths, R.B. Phase transitions in anisotropic classical Heisenberg ferromagnets. Commun.Math. Phys. 26, 102–108 (1972). https://doi.org/10.1007/BF01645697

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01645697

Keywords

Search

Navigation