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Prog. Theor. Phys. Vol. 51 No. 6 (1974) pp. 1694-1711

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Theory of One-Dimensional Random Mixture of Ising Spins

Fumitaka Matsubara

Department of Applied Physics, Tohoku University, Sendai

(Received November 8, 1973)

Abstract:

A general theory to obtain the magnetic properties of the one-dimensional random mixture of plural kinds of magnetic atoms (Ising spins) in the finite magnetic field is formulated in terms of distribution functions which give the probabilities of finding powers of average values of spins situated on the end site of the chain. The distribution functions are determined from the simultaneous functional equation of order n, where n is the number of the kind of magnetic atoms. Using this theory, we study the magnetic properties of the following systems: (1) The regular system composed of only one kind of magnetic atoms, (2) the simple random system composed of one kind of magnetic atoms and non-magnetic atoms, (3) the random binary mixture composed of two kinds of magnetic atoms of S = 1/2, (4) the random binary mixture of two kinds of magnetic atoms of S = 1/2 and S = 1. An Ising chain with random exchange integrals is also formulated in terms of a distribution function, and the magnetic properties are investigated when S = 1/2. It is shown that the magnetization curves of those mixtures at low temperatures have various steps when the antiferromagnetic elements are included, and the susceptibilities at H = 0 and T →0 diverge when the ferromagnetic elements are included even if the magnetization vanishes when T = 0 and H →0. Those are discussed in detail from the random nature of the mixtures.


URL : http://ptp.ipap.jp/link?PTP/51/1694/
DOI : 10.1143/PTP.51.1694

[ Full Text PDF : FREE ACCESS (1250K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 52 No. 4 (1974) pp. 1124-1134 :
    Theory of the Random Magnetic Mixture. I
    Fumitaka Matsubara
  2. Progress of Theoretical Physics Vol. 53 No. 6 (1975) pp. 1603-1616 :
    Theory of Random Magnetic Mixture. II
    Fumitaka Matsubara
  3. Progress of Theoretical Physics Vol. 54 No. 3 (1975) pp. 642-653 :
    Theory of Random Mixtures of Ising Spins
    Yohtaro Ueno and Takehiko Oguchi
  4. Progress of Theoretical Physics Vol. 55 No. 3 (1976) pp. 672-682 :
    Theory of Random Magnetic Mixture. III
    Fumitaka Matsubara and Masateru Sakata
  5. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1049-1063 :
    Random Mixture of the Ising Magnets in a Magnetic Field
    Shigetoshi Katsura
  6. Progress of Theoretical Physics Vol. 57 No. 6 (1977) pp. 1848-1861 :
    A New Cluster Approximation to the Diluted Ising and Heisenberg Ferromagnets
    Hiroshi Mano
  7. Progress of Theoretical Physics Vol. 58 No. 2 (1977) pp. 434-451 :
    Susceptibility and Specific Heat in the Glass-Like Phase
    Shigetoshi Katsura
  8. Progress of Theoretical Physics Supplement No.87 (1986) pp. 155-164 :
    Classical Limit of the Random Spin-One Ising Model on a Cayley Tree
    Colin J. Thompson, Sakari Inawashiro and Norman E. Frankel
  9. Progress of Theoretical Physics Supplement No.101 (1990) pp. 585-595 :
    Magnetic Phase Diagram of the Pseudo-Binary Ordered Alloy Fe(PdxPt1-x)3
    Makoto Kaburagi and Takashi Tonegawa

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