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Prog. Theor. Phys. Vol. 31 No. 3 (1964) pp. 412-423

[ Full Text PDF : FREE ACCESS (688K) ]

Cluster Expansion Theory for a System of Random Ising Spins

Ryuzo Abe

The Institute for Solid State Physics, The University of Tokyo, Azabu, Tokyo

(Received November 11, 1963)

Abstract:

The system under consideration is N Ising spins which interact through two-body exchange interactions and are randomly distributed over NL lattice points. By means of generalized cumulant expansion method, a statistical mechanical treatment of the system is made when the concentration p(=N/NL) is sufficiently low. Thermodynamic quantities are shown to be expressed in a form of cluster expansion similar to that in the theory of classical gases. As an application of the method, nearest neighbor ferromagnetic interactions are assumed, and the critical concentration below which there is no Curie temperature is calculated for some crystal structures and is compared with the results of other theories.


URL : http://ptp.ipap.jp/link?PTP/31/412/
DOI : 10.1143/PTP.31.412

[ Full Text PDF : FREE ACCESS (688K) ] Citation:

References:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 58 (1989) pp. 3219-3226 :
    High Temperature Expansion for the Ising Model on the Penrose Lattice
    Ryuzo Abe and Tomonari Dotera
  2. Journal of the Physical Society of Japan 59 (1990) pp. 2064-2077 :
    High Temperature Expansion for the Ising Model on the Dual Penrose Lattice
    Tomonari Dotera and Ryuzo Abe
  3. Progress of Theoretical Physics Vol. 36 No. 3 (1966) pp. 454-464 :
    Linked Cluster Expansion for a System with s-d Interaction
    Ryuzo Abe
  4. Progress of Theoretical Physics Vol. 36 No. 6 (1966) pp. 1083-1094 :
    A Statistical Model for the Dilute Ferromagnet
    Itiro Syozi and Sasuke Miyazima
  5. Progress of Theoretical Physics Vol. 84 No. 3 (1990) pp. 425-435 :
    Critical Compressibility Factor of Two-Dimensional Lattice Gas
    Ryuzo Abe, Tomonari Dotera and Takeshi Ogawa

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