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Prog. Theor. Phys. Vol. 55 No. 4 (1976) pp. 1049-1063

[ Full Text PDF : FREE ACCESS (877K) ]

Random Mixture of the Ising Magnets in a Magnetic Field

— Quenched Site and Bond Problems —

Shigetoshi Katsura

Department of Applied Physics, Faculty of Engineering, Tohoku University, Sendai 980

(Received August 16, 1975)

Abstract:

A method using projection operators developed in a previous paper [Can. J. Phys. 52 (1974), 120] to obtain the specific heat and the susceptibility of the random mixture of magnets, is applied for the low-field expansion of the free energy and the magnetization. The quartic terms of the free energies of the linear chain and of the infinite Bethe lattice for the site and the bond problems are obtained. The exact solution of the infinite Bethe lattice is equivalent to the Bethe approximation of the ordinary lattices. A divergence of the quartic term of the free energy of the bond problem is discussed in connection with a phase transition relating to the glass-like phase. Transparent formal similarity (which serves as a check and an outlook) between the site and the bond problem is found, and a relation (which serves as an approximation) between the quenched and the annealed systems is discussed.


URL : http://ptp.ipap.jp/link?PTP/55/1049/
DOI : 10.1143/PTP.55.1049

[ Full Text PDF : FREE ACCESS (877K) ] Citation:

References:

  1. S. Katsura and F. Matsubara, Can. J. Phys. 52 (1974), 120. In Eqs. [4·2] and [4·4], r.h.s. should be multiplied by mi. In Eqs. [4·3] and [4·4], Cij should read C.
    See also F. Matsubara, Prog. Theor. Phys. 51 (1974), 378[PTP].
  2. S. Katsura, Can. J. Phys. 53 (1975), 854.
  3. F. Matsubara, K. Yoshimura and S. Katsura, Can. J. Phys. 51 (1973), 1053.
    M. Wortis, Phys. Rev. B 10 (1974), 4665[APS].
  4. F. Matsubara and M. Sakata, Prog. Theor. Phys. 55 (1976), 672[PTP].
    a) S. Katsura, Prog. Theor. Phys. 20 (1958), 192[PTP]; ibid. 23 (1960), 967[PTP].
  5. F. Matsubara, Prog. Theor. Phys. 51 (1974), 1694[PTP].
  6. M. Kurata, R. Kikuchi and T. Watari, J. Chem. Phys. 21 (1953), 434[CrossRef].
  7. C. Domb, Adv. in Phys. 9 (1960), 283.
  8. S. Katsura and M. Takizawa, Prog. Theor. Phys. 51 (1974), 82[PTP].
  9. A. Pekalski and T. Oguchi, Prog. Theor. Phys. 54 (1975), 1021[PTP].
  10. Y. Kasai, S. Miyazima and I. Syozi, Prog. Theor. Phys. 42 (1969), 1[PTP].
    Y. Kasai and I. Syozi, Prog. Theor. Phys. 50 (1973), 1182[PTP].
  11. A. A. Lushnikov, Sov. Phys. -JETP 29 (1969), 120. [Zh. Eksp. Teor. Fiz. 56 (1969), 215].
  12. J. M. Kowalski and A. Pekalski, J. Phys. C 8 (1975), 2085. Their results (8) and (19) agree with our previous results in Ref. 1).

Citing Article(s) :

  1. Journal of the Physical Society of Japan 57 (1988) pp. 2310-2330 :
    Statistical Mechanical Theory of Cooperative Phenomena. II. Super-Effective-Field Theory with Applications to Exotic Phase Transitions
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  2. Progress of Theoretical Physics Vol. 55 No. 3 (1976) pp. 672-682 :
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  3. Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 683-685 :
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  4. Progress of Theoretical Physics Vol. 58 No. 1 (1977) pp. 362-364 :
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  5. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 434-451 :
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  6. Progress of Theoretical Physics Vol. 58 No. 4 (1977) pp. 1151-1165 :
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  7. Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 405-413 :
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  11. Progress of Theoretical Physics Vol. 63 No. 4 (1980) pp. 1098-1111 :
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  12. Progress of Theoretical Physics Vol. 63 No. 5 (1980) pp. 1800-1803 :
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  13. Progress of Theoretical Physics Vol. 64 No. 1 (1980) pp. 327-329 :
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  14. Progress of Theoretical Physics Vol. 65 No. 1 (1981) pp. 83-94 :
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  15. Progress of Theoretical Physics Vol. 65 No. 1 (1981) pp. 95-104 :
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  16. Progress of Theoretical Physics Vol. 65 No. 1 (1981) pp. 140-153 :
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  17. Progress of Theoretical Physics Vol. 66 No. 1 (1981) pp. 77-89 :
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  18. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1561-1573 :
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  19. Progress of Theoretical Physics Vol. 67 No. 2 (1982) pp. 689-692 :
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  20. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 20-31 :
    Hidden Mattis Phase in Annealed System
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  21. Progress of Theoretical Physics Vol. 74 No. 6 (1985) pp. 1175-1190 :
    Scaling Laws of the Nonlinear Part of Magnetization in the SK Model of Spin Glasses
    Makoto Katori and Masuo Suzuki
  22. Progress of Theoretical Physics Supplement No.69 (1980) pp. 69-79 :
    Lattice Gauge Theory for the Classical XY Model of Spin Glasses
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  23. Progress of Theoretical Physics Supplement No.80 (1984) pp. 195-202 :
    Frustration, Metastability and Nonlinear Susceptibility in Spin Glasses
    Masuo Suzuki
  24. Progress of Theoretical Physics Supplement No.87 (1986) pp. 139-154 :
    Theory of Spin Glass by the Method of the Distribution Function of an Effective Field
    Shigetoshi Katsura

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