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Prog. Theor. Phys. Vol. 20 No. 5 (1958) pp. 614-624

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Bose-Einstein Lattice Gases Equivalent to the Heisenberg Model of Ferro-, Antiferro- and Ferri-Magnetism

Tohru Morita

Physics Department, Tokyo Institute of Technology, Tokyo

(Received June 30, 1958)

Abstract:

The Hamiltonian are presented which are equivalent to the Heisenberg model of ferro-, antiferro- and ferri-magnetism and which have the form of finite power series of the Bose operators.
A technique for calculations of partition function for a system with such a Hamiltonian that contains a term of infinite potential is presented and discussed in connection with the theories of a ferromagnetic spin system by Van Kranendonk and Dyson.


URL : http://ptp.ipap.jp/link?PTP/20/614/
DOI : 10.1143/PTP.20.614

[ Full Text PDF : FREE ACCESS (550K) ] Citation:

References:

  1. J. Van Kranendonk and J. H. Van Vleck, Rev. Mod. Phys. 30 (1958), 1[APS].
  2. F. Bloch, Z. Phys. 61 (1930), 206; ibid. 74 (1932), 295.
  3. T. Holstein and H. Primakoff, Phys. Rev. 58 (1940), 1098[APS].
  4. R. Kubo, Phys. Rev. 87 (1952), 568[APS].
    T. Nagamiya, K. Yoshida and R. Kubo, Adv. Phys. 4 (1955), 1.
  5. P. W. Anderson, Phys. Rev. 86 (1952), 694[APS].
  6. T. Morita, Prog. Theor. Phys. 18 (1957), 462[PTP]; See also Ref. 7.
  7. T. Matsubara and H. Matsuda, Prog. Theor. Phys. 16 (1956), 569[PTP].
  8. H. Matsuda and T. Matsubara, Prog. Theor. Phys. 17 (1957), 19[PTP].
    H. Matsuda, Prog. Theor. Phys. 18 (1957), 357[PTP].
  9. J. Van Kranendonk, Physica 21 (1955), 749[CrossRef]; ibid. 21 (1955), 925[CrossRef].
  10. J. Van Kranendonk, Physica 21 (1955), 749[CrossRef]; ibid. 21 (1955), 925[CrossRef].
  11. F. J. Dyson, Phys. Rev. 102 (1956), 1217[APS]; ibid. 102 (1956), 1230[APS].
  12. F. J. Dyson, Phys. Rev. 102 (1956), 1217[APS]; ibid. 102 (1956), 1230[APS].
  13. Footnote 13 of Ref. 3.
  14. I. Mannari, Prog. Theor. Phys. 19 (1958), 201[PTP].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 64 (1995) pp. 1211-1216 :
    A Bose Lattice Gas Equivalent to Heisenberg Model and Its QCVM Study
    Tohru Morita
  2. Progress of Theoretical Physics Vol. 20 No. 5 (1958) pp. 728-736 :
    Bose-Einstein Lattice Gas Theory of Ferromagnetism
    Tohru Morita
  3. Progress of Theoretical Physics Vol. 27 No. 3 (1962) pp. 529-570 :
    Theory of Dynamical Behaviors of Ferromagnetic Spins
    Hazime Mori and Kyozi Kawasaki
  4. Progress of Theoretical Physics Vol. 92 No. 6 (1994) pp. 1081-1093 :
    An Approximation Scheme of the Cluster Variation Method for Quantum Lattice Gases
    Tohru Morita
  5. Progress of Theoretical Physics Vol. 94 No. 1 (1995) pp. 1-9 :
    A Lattice-Gas Model Equivalent to the t-J Model
    Tohru Morita

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