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Journal of Statistical Physics

, Volume 89, Issue 5–6, pp 1035–1046 | Cite as

Dynamic Behavior of a Spin- 1 Ising Model. I. Relaxation of Order Parameters and the “Flatness” Property of Metastable States

  • Mustafa Keskin
  • Riza Erdem
Articles

Abstract

The dynamic behavior of a spin-1 Ising system with arbitrary bilinear and biquadratic pair interactions is studied by using the path probability method, and approaches of the system toward the stable or metastable equilibrium states according to the ratio of interaction parameters and rate constants are presented. In particular, we investigate the relaxation of the order parameters for temperatures less than, equal to, and greater than the second-order and first-order phase transitions. From this investigation, the “flatness” property of metastable states is seen explicitly. We also show how a system freezes in a metastable state as well as how it escapes from one metastable state to the other.

Key words

Spin-1 Ising system path probability method metastable states relaxation curves 

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References

  1. 1.
    M. Blume, V. J. Emery and R. B. Griffiths,Phys. Rev. A 4:1071 (1971).CrossRefADSGoogle Scholar
  2. 2.
    L. Lajzerowicz and J. Sivardière,Phys. Rev. A 11:2079 (1973); J. Sivardière and L. Lajzerowicz,ibid. 11:2090 (1975).CrossRefADSGoogle Scholar
  3. 3.
    J. Sivardière and L. Lajzerowicz,Phys. Rev. A 11:2101 (1975).CrossRefADSGoogle Scholar
  4. 4.
    M. Shick and W. H. Shih,Phys. Rev. B 34:1797 (1986).CrossRefADSGoogle Scholar
  5. 5.
    K. E. Newman and J. D. Dow,Phys. Rev. B 27:7495 (1983).CrossRefADSGoogle Scholar
  6. 6.
    S. A. Kivelson, V. J. Emery, and H. Q. Lin,Phys. Rev. B 62:6523 (1990).CrossRefADSGoogle Scholar
  7. 7.
    H. H. Chen and P. M. Levy,Phys. Rev. B 7:4267 (1973).CrossRefADSGoogle Scholar
  8. 8.
    I. Fittipaldi and A. F. Siqueria,J. Magn. Magn. Mat. 54-57:646 (1986); K. G. Chakraborty,J. Phys. C 21:2911 (1987).CrossRefADSGoogle Scholar
  9. 9.
    A. N. Berker and M. Wortis,Phys. Rev. B 14:4946 (1976); W. Hoston and A. N. Berker,J. Appl. Phys. 70:6101 (1991).CrossRefADSGoogle Scholar
  10. 10.
    W. Hoston and A. N. Berker,Phys. Rev. Lett. 67:1027 (1991); M. E. S. Borelli and C. E. I. Carneiro,Physica 230A:249 (1996); C. Temirci, A. KokÇe and M. Keskin,Physica 231A:673 (1996).CrossRefADSGoogle Scholar
  11. 11.
    A. K. Jain and D. P. Landau,Phys. Rev. B 22:445 (1980); Y. L. Wang and C. Wentworth,J. Apply. Phys. 61:4411 (1987); Y. L. Wang, F. Lee, and J. D. Kimel,Phys. Rev. B 36:8945 (1987).CrossRefADSGoogle Scholar
  12. 12.
    A. Rosengren and S. Lapinskas,Phys. Rev. B 47:2643 (1993); S. Lapinskas and A. Rosengren,ibid. 49:15190 (1994).CrossRefADSGoogle Scholar
  13. 13.
    M. Keskin, Ş. özgan,Phys. Lett. A 145:340 (1990).CrossRefADSGoogle Scholar
  14. 14.
    M. Keskin, M. An and Ş. özgan,Tr. J. of Phys. 15:575 (1991).Google Scholar
  15. 15.
    M. Keskin,Physica Scripta 47:328 (1993); M. Keskin and A. ErdinÇ,Tr. J. of Phys. 19:88 (1995); M. Keskin and H. Arslan,ibid. 19:408 (1995);J. Magn. Magn. Mat. 146:L247 (1995).CrossRefADSGoogle Scholar
  16. 16.
    R. Ballou, C. Lacroix, and M. D. Nunez-Reguerro,Phys. Rev. Lett. 66:1910 (1991).CrossRefADSGoogle Scholar
  17. 17.
    T. Obakata,J. Phys. Soc. Jpn. 26:895 (1969).CrossRefADSGoogle Scholar
  18. 18.
    M. Tanaka and K. Takahashi,Prog. Theor. Phys. 58:387 (1977);J. Phys. Soc. Jpn. 43:1832 (1977).CrossRefADSGoogle Scholar
  19. 19.
    G. L. Batten, Jr. and H. L. Lemberg,J. Chem. Phys. 70:2934 (1979).CrossRefADSGoogle Scholar
  20. 20.
    Y. Saito and H. Müller-Krumbhaar,J. Chem. Phys. 74:721 (1981).CrossRefADSGoogle Scholar
  21. 21.
    Y. Achiam,Phys. Rev. B 31:260 (1985).CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    M. Keskin and P.H. E. Meijer,Physica 122A:1 (1983); M. Keskin,ibid 135:226 (1986).ADSGoogle Scholar
  23. 23.
    M. Keskin and P. H. E. Meijer,J. Chem. Phys. 85:7324 (1986).CrossRefADSGoogle Scholar
  24. 24.
    M. Keskin, M. An and P. H. E. Meijer,Physica 157A:1000 (1989).ADSGoogle Scholar
  25. 25.
    R. Kikuchi,Supply. Progr. Theo. Phys. 35:1 (1966).CrossRefADSGoogle Scholar
  26. 26.
    M. Keskin and P. H. E. Meijer,Phys. Rev. E. 55:5343 (1997).CrossRefADSGoogle Scholar
  27. 27.
    R. Kikuchi,Phys. Rev. 81:988 (1951); H. ŞiŞman and M. Keskin,Tr. J. Phys. 14:88 (1990).MATHCrossRefADSMathSciNetGoogle Scholar
  28. 28.
    H. E. Stanley, “Introductionto Phase Transitions and Critical Phenomena” (Oxford University Press, New York, 1971).Google Scholar
  29. 29.
    R. J. Glauber,J. Math. Phys. 4:294 (1963).MATHCrossRefADSMathSciNetGoogle Scholar
  30. 30.
    K. Binder,Phys. Rev. B 8:3423 (1973).CrossRefADSGoogle Scholar
  31. 31.
    H. Sato and R. Kikuchi,Acta Metallurgica 24:797 (1976).CrossRefGoogle Scholar
  32. 32.
    P. H. E. Meijeŕ and M. Keskin,J. Phys. Chem. Solids 45:955(1984).CrossRefGoogle Scholar
  33. 33.
    P. Hanggi, P. Talkner and M. Borkovec,Rev. Mod. Phys. 62:251 (1990).CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Mustafa Keskin
    • 1
  • Riza Erdem
    • 2
  1. 1.Department of PhysicsErciyes UniversityKayseriTurkey
  2. 2.Department of PhysicsGaziosmanpaŞa UniversityTokatTurkey

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