HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 41 (1969) > Number 4
| Next Article >

Prog. Theor. Phys. Vol. 41 No. 4 (1969) pp. 941-948

[ Full Text PDF : FREE ACCESS (472K) ]

Dynamics of the Ising Model near the Transition Point. II

Ryuzo Abe and Akira Hatano

Department of Pure and Applied Sciences, College of General Education, University of Tokyo, Komaba, Meguro-ku, Tokyo

(Received October 11, 1968)

Abstract:

The Isin spin system is discussed in which the interaction of spins with a heat bath causes the spontaneous flip of spins. A treatment discussed in a previous paper for the square lattice is extended to the honeycomb and triangular lattices. In the case of honeycomb lattice, an additional term to the one studied in the previous paper is calculated explicitly at the transition point and an exact expansion is derived for the dynamic susceptibililty χ(ω) up to the term of the order of 1/ω2. Some discussions are given of the low frequency behavior of χ(ω) on the basis of variational principle.


URL : http://ptp.ipap.jp/link?PTP/41/941/
DOI : 10.1143/PTP.41.941

[ Full Text PDF : FREE ACCESS (472K) ] Citation:

References:

  1. R. Abe, Prog. Theor. Phys. 39 (1968), 947[PTP].
  2. R. J. Glauber, J. Math. Phys. 4 (1963), 294[CrossRef].
  3. R. M. F. Houtappel, Physica 16 (1950), 425[CrossRef].
  4. G. A. T. Allan and D. D. Betts, Can. J. Phys. 46 (1968), 15.
  5. M. E. Fisher, Phys. Rev. 113 (1959), 969[APS].
  6. J. Stephenson, J. Math. Phys. 5 (1964), 1009[CrossRef].
  7. M. Suzuki and R. Kubo, J. Phys. Soc. Jpn. 24 (1968), 51[JPSJ].
  8. See for example, A. H. Wilson, The Theory of Metals (Cambridge University Press, New York, 1953), p. 251.
  9. B. I. Halperin and P. C. Hohenberg, Phys. Rev. Lett. 19 (1967), 700[APS].
    K. Kawasaki, Prog. Theor. Phys. 39 (1968), 1133[PTP]; ibid. 40 (1968), 35[PTP].
    H. Mori and H. Okamoto, Phys. Lett. A 26 (1968), 285.
  10. K. Kawasaki, Phys. Rev. 143 (1966), 375[APS].
    L. P. Kadanoff and J. Swift, Phys. Rev. 165 (1968), 310[APS].
  11. M. Suzuki, H. Ikari and R. Kubo, Proceedings of the International Conference on Statistical Mechanics, Kyoto (1968), p. 153.
  12. P. W. Kasteleyn, J. Math. Phys. 4 (1963), 287[CrossRef].
    E. W. Montroll, R. B. Potts and J. C. Ward, J. Math. Phys. 4 (1963), 308[CrossRef].
    M. E. Fisher, J. Math. Phys. 7 (1966), 1776[CrossRef].
  13. K. Kano, Prog. Theor. Phys. 35 (1966), 1[PTP].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 43 No. 4 (1970) pp. 882-906 :
    On the Singularity of Dynamical Response and Critical Slowing Down
    Masuo Suzuki
  2. Progress of Theoretical Physics Vol. 63 No. 1 (1980) pp. 42-50 :
    Pseudo-Critical Phenomena in the Fisher-Domb Cluster Model
    Hiroshi Ikeda
  3. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 20-31 :
    Hidden Mattis Phase in Annealed System
    Yasuhiro Kasai and Ayao Okiji

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.