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Prog. Theor. Phys. Vol. 54 No. 3 (1975) pp. 642-653

[ Full Text PDF : FREE ACCESS (973K) ]

Theory of Random Mixtures of Ising Spins

Yohtaro Ueno and Takehiko Oguchi

Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152

(Received December 4, 1974)

Abstract:

Magnetic properties of the annealed quenched systems each in the bond and site models are investigated by the Kikuchi pair approximation. In the annealed system, phase diagrams and susceptibilities are obtained. Two critical temperatures in some case in the bond system and no critical concentration in the site system are obtained. The physical interpretation of them is given. In the quenched system, two different approximate conditions are considered for the complete randomness. The case of the first condition is equivalent to the cluster variation method proposed by Sato, Arrott and Kikuchi, and the results are in agreement with those obtained by Katsura and Matsubara. The second is essentially equivalent to the average coordination number method by Sato, Arrott and Kikuchi for the dilute ferromagnetism. However, the results for both cases are unreliable at low temperatures, because of the appearance of negative entropy. This is inevitable under the pair condition.


URL : http://ptp.ipap.jp/link?PTP/54/642/
DOI : 10.1143/PTP.54.642

[ Full Text PDF : FREE ACCESS (973K) ] Citation:

References:

  1. Y. Kasai, S. Miyazima and I. Syozi, Prog. Theor. Phys. 42 (1969), 1[PTP].
    See also Y. Kasai and I. Syozi, Prog. Theor. Phys. 50 (1973), 1182[PTP].
  2. F. Matsubara, Prog. Theor. Phys. 51 (1974), 378[PTP]; ibid. 51 (1974), 1694[PTP].
  3. F. Matsubara, Prog. Theor. Phys. 52 (1974), 1124[PTP].
  4. S. Katsura and F. Matsubara, Can. J. Phys. 52 (1974), 120.
  5. R. Kikuchi, Phys. Rev. 81 (1951), 988[APS].
  6. H. Sato, A. Arrott and R. Kikuchi, J. Phys. Chem. Solids 10 (1959), 19[CrossRef].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 57 (1988) pp. 156-165 :
    Phase Transitions Due to Entropy Gains in Layered Periodic Potts Models on a Square Lattice
    Gang Sun, Yohtaro Ueno and Yukiyasu Ozeki
  2. Journal of the Physical Society of Japan 58 (1989) pp. 3106-3110 :
    Ising Model with Even-Bonds Plaquettes on the Square Lattice
    Tsuyoshi Horiguchi
  3. Progress of Theoretical Physics Vol. 55 No. 3 (1976) pp. 672-682 :
    Theory of Random Magnetic Mixture. III
    Fumitaka Matsubara and Masateru Sakata
  4. Progress of Theoretical Physics Vol. 56 No. 6 (1976) pp. 1669-1673 :
    One-Dimensional Random Annealed Ising Spin System on the Site Model
    Shunichi Muto and Takehiko Oguchi
  5. Progress of Theoretical Physics Vol. 57 No. 5 (1977) pp. 1497-1506 :
    An Ising Model for Magnetic Mixture Composed of Triangle-Bond Elements
    Yasuhiro Kasai
  6. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 434-451 :
    Susceptibility and Specific Heat in the Glass-Like Phase
    Shigetoshi Katsura
  7. Progress of Theoretical Physics Vol. 59 No. 5 (1978) pp. 1437-1446 :
    Monte Carlo Simulation for Random Mixtures of a Three-Dimensional Ising Site Model. II
    Takeshi Tatsumi
  8. Progress of Theoretical Physics Supplement No.87 (1986) pp. 180-190 :
    Potts and Related Glasses
    David Sherrington

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