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Prog. Theor. Phys. Vol. 20 No. 2 (1958) pp. 192-215

[ Full Text PDF : FREE ACCESS (939K) ]

Cluster Sums and Related Coefficients of the Ising Model

Shigetoshi Katsura

Department of Applied Science, Tohoku University, Sendai

(Received April 26, 1958)

Abstract:

It is the purpose of the present paper to discuss the intuitive meaning and the interrelations of various coefficients of the Ising model. Thus, the intuitive meaning of blm and blm, the coefficients of cluster sums, is explained. Van der Waerden-Oguchi's expansion is generalized to the case with magnetic field and the coefficients Ωnm is defined and its meaning is explained. The equivalence of the calculation of the susceptibility with zero field and the non-crossing chain problem is proved. And a method of evaluation of these coefficients is proposed which requires least labour of counting the graphs by using the decomposition of Fuch's coefficients γk.
The data our calculations are listed in the Appendix. From these data an outlook of this problem to the future and the theory of the imperfect gases are discussed.


URL : http://ptp.ipap.jp/link?PTP/20/192/
DOI : 10.1143/PTP.20.192

[ Full Text PDF : FREE ACCESS (939K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 61 (1992) pp. 1127-1131 :
    Irreducible Cluster Sums and the Virial Coefficients for Lattice Gases
    Kunisuke Nisizima and Kazuyosi Ikeda
  2. Progress of Theoretical Physics Vol. 53 No. 2 (1975) pp. 326-348 :
    Volume-Dependent Cluster Sums for Lattice Gases. I
    Kazuyosi Ikeda and Kunisuke Nisizima
  3. Progress of Theoretical Physics Vol. 55 No. 4 (1976) pp. 1049-1063 :
    Random Mixture of the Ising Magnets in a Magnetic Field
    Shigetoshi Katsura
  4. Progress of Theoretical Physics Vol. 56 No. 4 (1976) pp. 1056-1072 :
    Volume-Dependent Cluster Sums for Lattice Gases. III
    Kazuyosi Ikeda and Kunisuke Nisijima

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