Skip to main content
Log in

On the Onsager-Yang-Value of the spontaneous magnetization

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

Abstract

We show that the value of the spontaneous magnetization for the two-dimensional Ising model computed by Onsager is indeed, the appropriate derivative of the free energy with respect to the magnetic field. The argument is based on a simple application of the duality transformation.

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. Onsager, L.: Suppl. Nuovo Cimento6, 261 (1949).

    Google Scholar 

  2. Yang, C. N.: Phys. Rev.85, 809 (1952).

    Google Scholar 

  3. Montroll, E. W., Potts, R. B., Ward, J. C.: J. Math. Phys.4, 308 (1963); see also: Schultz, T. D., Mattis, D.C., Lieb, E.H.: Rev. Mod. Phys.36, 856 (1964).

    Google Scholar 

  4. Griffiths, R. B.: Phys. Rev.152, 240 (1966).

    Google Scholar 

  5. Lebowitz, J. L., Martin-Lof, A.: Commun. math. Phys.25, 276 (1972).

    Google Scholar 

  6. Lebowitz, J. L.: Commun. math. Phys.28, 313 (1972).

    Google Scholar 

  7. Martin-Löf, A.: Commun. math. Phys.20, 253 (1972); see also: Gallavotti, G., Miracle, S.: Phys. Rev.B5, 2555 (1972).

    Google Scholar 

  8. Kramers, H. A., Wannier, G. H.: Phys. Rev.60, 252 (1941).

    Google Scholar 

  9. Domb, C.: Adv. Phys.9, 149 (1960).

    Google Scholar 

  10. Fisher, M. E., Ferdinand, A. E.: Phys. Rev. Lett.19, 169 (1967).

    Google Scholar 

  11. Kadanoff, L. P., Ceva, H.: Phys. Rev.B3, 3918 (1971).

    Google Scholar 

  12. Benettin, G., Jona-Lasinio, G., Stella, A. L.: Lett. Nuovo Cimento4, 443 (1972) and paper in preparation.

    Google Scholar 

  13. Gallavotti, G.: La Rivista del Nuovo Cimento2, 133 (1972).

    Google Scholar 

  14. Gallavotti, G.: Commun. math. Phys.27, 103 (1972).

    Google Scholar 

  15. Dobrushin, R. L.: preprint (1972), Moscow: “Gibbs states. Description of phase Coexistence in the 3-dimensional Ising model.”

  16. In this appendix for convenience of the reader we give a treatment of duality suitable for the purpose of the present paper. It should be mentioned however, that it contains certain remarks on the role of boundary conditions which do not appear in full detail elsewhere in the literature. For recent formulations of duality in the case of more general models see Wegner, F. J.: J. Math. Phys.12, 2259 (1971); — Merlini, D., Gruber, C.: preprint (1972).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Lavoro eseguito nell'ambito del G.N.F.M.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Benettin, G., Gallavotti, G., Jona-Lasinio, G. et al. On the Onsager-Yang-Value of the spontaneous magnetization. Commun.Math. Phys. 30, 45–54 (1973). https://doi.org/10.1007/BF01646687

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01646687

Keywords

Navigation