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Prog. Theor. Phys. Vol. 51 No. 2 (1974) pp. 378-390

[ Full Text PDF : FREE ACCESS (1033K) ]

Magnetic Properties of Random Mixture of the One-Dimensional Ising Chain

Fumitaka Matsubara

Department of Physics, Tohoku University, Sendai

(Received July 26, 1973)

Abstract:

The susceptibilities of both the one-dimensional random Ising chain and the random Ising Bethe lattice composed of plural kinds of magnetic atoms of S = 1/2 and non-magnetic atoms are studied based on a new method, i.e., by using simultaneous linear equation of order n, where n is the number of kinds of magnetic atoms. The susceptibilities of the binary and ternary systems, which correspond to n = 1 and 2, respectively, are exactly obtained for both the one-dimensional chain and the Bethe lattice. The critical temperature of the random Bethe lattice is also obtained. It is shown that the critical temperature of the binary Bethe lattice is in agreement with that of the ordinary two- or three-dimensional lattice in the cluster variation method and that the critical temperature of the ternary Bethe lattice is independent of the signs of exchange integrals. It is also conjectured that the critical temperature of the ordinary ternary system does not depend on the signs of exchange integrals when two kinds of magnetic atoms are of the same type and the lattice structure is loose-packed. The problem of the random exchange integrals is also discussed.


URL : http://ptp.ipap.jp/link?PTP/51/378/
DOI : 10.1143/PTP.51.378

[ Full Text PDF : FREE ACCESS (1033K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 51 No. 6 (1974) pp. 1694-1711 :
    Theory of One-Dimensional Random Mixture of Ising Spins
    Fumitaka Matsubara
  2. Progress of Theoretical Physics Vol. 52 No. 4 (1974) pp. 1124-1134 :
    Theory of the Random Magnetic Mixture. I
    Fumitaka Matsubara
  3. Progress of Theoretical Physics Vol. 52 No. 6 (1974) pp. 1798-1806 :
    Percolation Theory and the Ising Model for a Class of Triangular Cactii
    A. R. Bishop
  4. Progress of Theoretical Physics Vol. 53 No. 1 (1975) pp. 50-65 :
    A Use of Bethe Lattice Solutions for Percolation-Constrained Phenomena
    A. R. Bishop
  5. Progress of Theoretical Physics Vol. 54 No. 3 (1975) pp. 642-653 :
    Theory of Random Mixtures of Ising Spins
    Yohtaro Ueno and Takehiko Oguchi
  6. Progress of Theoretical Physics Vol. 54 No. 4 (1975) pp. 1021-1027 :
    Random Mixtures in Annealed and Quenched Ising Bond Model
    Andrzej Pekalski and Takehiko Oguchi
  7. Progress of Theoretical Physics Vol. 55 No. 3 (1976) pp. 672-682 :
    Theory of Random Magnetic Mixture. III
    Fumitaka Matsubara and Masateru Sakata
  8. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1049-1063 :
    Random Mixture of the Ising Magnets in a Magnetic Field
    Shigetoshi Katsura
  9. Progress of Theoretical Physics Vol. 57 No. 1 (1977) pp. 28-41 :
    Thermodynamic Properties of the Frozen System
    Yoshimasa Itoh and Kiyoshi Teramoto
  10. Progress of Theoretical Physics Vol. 57 No. 2 (1977) pp. 683-685 :
    Comments on the Papers by Katsura and by Matsubara and Sakata about the Theory of Random Quenched Mixtures
    Takehiko Oguchi and Yohtaro Ueno
  11. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 434-451 :
    Susceptibility and Specific Heat in the Glass-Like Phase
    Shigetoshi Katsura
  12. Progress of Theoretical Physics Supplement No.87 (1986) pp. 180-190 :
    Potts and Related Glasses
    David Sherrington

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