Skip to main content
Log in

Phase diagrams of lattice systems with residual entropy

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We introduce an equivalence relation on the family of ground states and generalize the Peierls and Pirogov-Sinai theory of phase transitions to systems with residual entropy. The idea consists in the replacement of the periodic ground states by equivalence classes together with an entropy factor. We apply these results to discuss the phase diagrams of diluted spin-1/2 systems.

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. R. Peierls,Proc. Camb. Philos. Soc. 32:427 (1936).

    Google Scholar 

  2. R. B. Griffiths, inPhase Transition and Critical Phenomena, Vol. 1, C. Domb and M. S. Green, eds. (Academic Press, New York, 1972).

    Google Scholar 

  3. Ya. G. Sinai,Theory of Phase Transition, Rigorous Results (Pergamon, New York, 1982).

    Google Scholar 

  4. J. Slawny, inPhase Transition and Critical Phenomena, Vol. 10, C. Domb and J. C. Lebowitz, eds. (Academic Press, New York, 1987).

    Google Scholar 

  5. A. Sütö,J. Stat. Phys. 23:203 (1980);Helv. Phys. Acta 54:191, 201 (1981);J. Phys. A 14:2733 (1981); for a review see R. Liebmann,Statistical Mechanics of Periodic Frustrated Ising Systems (Springer, 1986).

    Google Scholar 

  6. E. I. Dinaburg and Ya. G. Sinai,Commun. Math. Phys. 98:119 (1985); E. I. Dinaburg and A. E. Mazel, in8th International Congress on Mathematical Physics, M. Mebkhout and R. Séneor, eds. (World Scientific, Singapore, 1987).

    Google Scholar 

  7. J. L. Lebowitz, M. K. Phani, and D. F. Styer,J. Stat. Phys. 38:413 (1985).

    Google Scholar 

  8. J. Bricmont, K. Kuroda, and J. L. Lebowitz,Commun. Math. Phys. 101:501 (1985).

    Google Scholar 

  9. J. Bricmont and J. Slawny, inStatistical Mechanics and Field Theory: Mathematical Aspects (Springer, 1986).

  10. R. B. Griffiths,Physica 33:689 (1967).

    Google Scholar 

  11. C. Gruber, A. Hintermann, and D. Merlini,Group Analysis of Classical Lattice Systems (Springer, 1977).

  12. J. Bernasconi and F. Rys,Phys. Rev. B 4:3045 (1977).

    Google Scholar 

  13. M. W. Capel,Physica 32 966 (1966).

    Google Scholar 

  14. M. Blume, V. J. Emery, and R. B. Griffiths,Phys. Rev. A 4:1071 (1971).

    Google Scholar 

  15. D. Mukamel and M. Blume,Phys. Rev. A 10:610 (1974).

    Google Scholar 

  16. Z. Racz and T. Vicsek,Phys. Rev. B 27:2992 (1983).

    Google Scholar 

  17. J. R. Banavard and F. Y. Wu,Phys. Rev. B 29:1511 (1984).

    Google Scholar 

  18. Y. Saito,J. Chem. Phys. 74:713 (1981).

    Google Scholar 

  19. J. Jedrzejewski,Z. Phys. B 59:325 (1985).

    Google Scholar 

  20. V. Schmid, Etude Numérique du diagramme de phase du modèle de Hubbard, Diploma Thesis EPF-L (1986), unpublished.

Download references

Author information

Authors and Affiliations

Authors

Additional information

On leave of absence from the Central Research Institute for Physics, Budapest, Hungary.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gruber, C., Sütö, A. Phase diagrams of lattice systems with residual entropy. J Stat Phys 52, 113–142 (1988). https://doi.org/10.1007/BF01016407

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01016407

Key words

Navigation