Journal of Statistical Physics

, Volume 61, Issue 1–2, pp 121–141 | Cite as

Superdegenerate point in FCC phase diagram: CVM and Monte Carlo investigations

  • R. Tétot
  • A. Finel
  • F. Ducastelle


We investigate the topology of the phase diagram of binary alloys on the fee lattice with first-neighbor antiferromagnetic interactions around the superdegenerate point, where the L10 and L12 phases meet. We treat the system as a “hard-constraint lattice gas,” following a procedure previously described by Lebowitzet al. We perform cluster variation method calculations in theT→0 limit and Monte Carlo simulations directly atT=0 K on the ground states of the superdegenerate point. We find that: (i) there is no disordered phase in the neighborhood of this point; (ii) a phase L′ for which two of the four cubic sublattices have the same average occupancy and each of the two others are different appears between L10 and L12; (iii) the transition L′/L12 is of first order.

Key words

Ising model superdegenerate ground states cluster variation method Monte Carlo simulations constrained lattice gas 


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  1. 1.
    K. Binder,Phys. Rev. Lett. 45:811 (1980).Google Scholar
  2. 2.
    K. Binder, J. L. Lebowitz, M. K. Phani, and M. H. Kalos,Phys. Rev. B 21:4027 (1980).Google Scholar
  3. 3.
    K. Binder, J. L. Lebowitz, M. K. Phani, and M. H. Kalos,Acta Met. 29:1655 (1981).Google Scholar
  4. 4.
    D. de Fontaine and R. Kikuchi,Nat. Bur. Std. SP 496:999 (1977).Google Scholar
  5. 5.
    J. M. Sanchez, D. de Fontaine, and W. Teitler,Phys. Rev. B 26:1465 (1982).Google Scholar
  6. 6.
    J. L. Lebowitz, M. K. Phani, and D. F. Styer,J. Stat. Phys. 38:413 (1985).Google Scholar
  7. 7.
    U. Gahn,J. Phys. Chem. Solids 43:977 (1982).Google Scholar
  8. 8.
    U. Gahn,J. Phys. Chem. Solids 47:1153 (1986).Google Scholar
  9. 9.
    H. Ackermann, S. Crusius, and G. Inden,Acta Met. 34:2311 (1986).Google Scholar
  10. 10.
    H. T. Diep, A. Ghazali, B. Berge, and P. Lallemand,Europhys. Lett. 2:603 (1986).Google Scholar
  11. 11.
    A. Finel and F. Ducastelle,Europhys. Lett. 1:135 (1986); erratum1:543 (1986).Google Scholar
  12. 12.
    R. Kikuchi,Prog. Theor. Phys. Suppl. 87:69 (1986).Google Scholar
  13. 13.
    A. Finel, inAlloy Phase Stability, G. M. Stocks and A. Gonis, eds. (Kluwer, Dordrecht, 1989).Google Scholar
  14. 14.
    W. Shockley,J. Chem. Phys. 6:130 (1938).Google Scholar
  15. 15.
    A. Danielian,Phys. Rev. 133:1344 (1964).Google Scholar
  16. 16.
    D. Styer, M. K. Phani, and J. L. Lebowitz,Phys. Rev. B 34:3361 (1986).Google Scholar
  17. 17.
    Y. G. Sinaï,Theory of Phase Transitions: Rigourous Results (Pergamon Press, Oxford, 1982).Google Scholar
  18. 18.
    J. Slawny,J. Stat. Phys. 20:711 (1979).Google Scholar
  19. 19.
    J. Slawny, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1987).Google Scholar
  20. 20.
    A. Finel, Thesis, Université Pierre et Marie Curie, Paris, France (1987).Google Scholar
  21. 21.
    J. Bricmont and J. Slawny,J. Stat. Phys. 54:89 (1989).Google Scholar
  22. 22.
    H. Meirovitch,Phys. Rev. B 30:2866 (1984).Google Scholar
  23. 23.
    N. A. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller,J. Chem. Phys. 21:1087 (1953).Google Scholar
  24. 24.
    Y. Saito, K. Furuta, and M. Hoyou,J. Phys. Soc. Japan 56:178 (1987).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • R. Tétot
    • 1
  • A. Finel
    • 1
  • F. Ducastelle
    • 1
  1. 1.ONERAChatillon CedexFrance

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