HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 65 (1981) > Number 1
| Next Article >

Prog. Theor. Phys. Vol. 65 No. 1 (1981) pp. 172-189

[ Full Text PDF : FREE ACCESS (689K) ]

Classical Planar Heisenberg Ferromagnet, Complex Scalar Field and Nonlinear Excitations

Shozo Takeno and Shigeo Homma*

Department of Physics, Kyoto Technical University, Kyoto 606
*Department of Applied Physics, Faculty of Engineering, Nagoya University, Nagoya 464

(Received September 8, 1980)

Abstract:

Nonlinear excitations in a classical planar Heisenberg ferromagnet in an external field (CPHFF) are studied. Taking a classical counterpart of the spin-raising operator as a relevant field variable, we establish a close correspondence between the CPHFF and a complex scalar field (CSF) in which each atom in a complex lattice field, while coupled with its neighbours, sits on ψ4-like on-site potential with saturable nonlinearity; In their static form CPHFF equations and CSF equations are identical to each other. In the continuum limit the CSF takes a semi-classical form of a Bose liquid with nonlinearity, however, characteristic of classical spin system. Solutions to the field equations are studied by using the continuum approximation. In one-dimensional case moving domain-wall solutions associated with symmetry-breaking states are obtained for the CPHFF and the CSF. In two- and three-dimensional cases static solutions to the field equations are obtained in the form of vortex solutions in close analogy to the case of the Ginzburg-Pitaevskii equation in the theory of superfluidity.


URL : http://ptp.ipap.jp/link?PTP/65/172/
DOI : 10.1143/PTP.65.172

[ Full Text PDF : FREE ACCESS (689K) ] Citation:

References:

  1. D. D. Betts, Phase Transitions and Critical Phenomena, eds. C. Domb and M. S. Green (Academic Press, London, New York, 1974), vol. 3, p. 569, and also references cited therein.
  2. E. Lieb, T. Schults and D. Mattis, Ann. of Phys. 16 (1961), 407[CrossRef].
  3. S. Katsura, Phys. Rev. 127 (1962), 1508[APS].
  4. P. Pfeuty, Ann. of Phys. 57 (1970), 79[CrossRef].
  5. T. Matsubara and H. Matsuda, Prog, Theor. Phys. 16 (1956), 569.
    See also, R. T. Whitlock and P. R. Zilsel, Phys. Rev. 131 (1963), 2409[APS].
    M. E. Fisher, Rep. on Prog. Phys. 30 (1967), 615.
  6. B. I. Halperin and P. C. Hohenberg, Phys. Rev. 188 (1969), 898[APS].
    See also, C. P. Enz, Rev. Mod. Phys. 46 (1974), 705[APS].
  7. Y. Nagaoka, in “Physics of Highly Excited States in Solids”, Lecture Notes in Phys. No. 57, eds. M. Ueta and Y. Nishina (Springer-Verlag, Berlin, Heiderberg, New York, 1976), p.137.
  8. M. Lakshmanan, Phys. Lett. A 61 (1977), 53[CrossRef].
  9. V. E. Zakharov and L. A. Takhtajan, Theor. Math. Phys. 38 (1979), 17.
    L. A. Takhtajan, Phys. Lett. A 64 (1977), 235[CrossRef].
  10. E. K. Sklyanin. LOME Preprint-E-3-79, Leningrad, 1979.
  11. A. E. Borovik, Solid State Commun. 34 (1980), 721[CrossRef].
  12. S. Takeno and S. Homma, Prog. Theor. Phys. 64 (1980), 1193[PTP].
  13. V. L. Ginzburg and L. P. Pitaevskii, Sov. Phys. -JETP 34 (1958), 1240.
    L. P. Pitaevskii, Sov. Phys. -JETP 40 (1961), 646.
    E. P. Gross, J. Math. Phys. 4 (1963), 195[CrossRef].
  14. R. J. Glauber and F. Haake, Phys. Rev. A 13 (1976), 357[APS].
  15. A. A. Belavin and A. M. Polyakov, JETP Lett. 22 (1975), 245.
  16. F. J. Ernst, Phys. Rev. 167 (1968), 1175[APS].
    See also, T. Tomimatsu and H. Sato, Prog, Theor. Phys. 50 (1973), 95.
  17. J. S. Langer, Phys. Rev. 167 (1968), 183[APS]; ibid. 184 (1969), 219[APS].
  18. P. W. Anderson, Rev. Mod. Phys. 38 (1966), 298[APS].
  19. S. Homma and S. Takeno, J. Phys. Soc. Jpn. 49 (1980), 1671[JPSJ].
  20. J. M. Radcliffe, J. of Phys. A 4 (1971), 313[CrossRef].
    See also, F. T. Arecchi, E. Courtens, R. Gilmore and H. Thomas, Phys. Rev. A 6 (1972), 2211[APS].
  21. S. Takeno, J. Phys. Soc. Jpn. 48 (1980), 1075[JPSJ].
  22. T. Tsuzuki, J. Low Temp. Phys. 41 (1971), 441.
  23. A. Hasegawa and F. Tappert, Appl. Phys. Lett. 23 (1973), 171[CrossRef].
  24. R. Hirota, in “Bäcklund Transformations, the Inverse Scattering Method, Solitons and their Applications”, Lecture Notes in Mathematics, No. 515, ed R. M. Miura (Springer, New York, 1976), p. 40.
  25. S. Hikami and T. Tsuneto, Prog. Theor. Phys. 63 (1980), 387[PTP].
  26. T. D. Lee, Phys. Rep. C 23 (1976), 254[CrossRef].
  27. See also, V. E. Zakharov and A. B. Shabat, Sov. Phys. -JETP 34 (1972), 62.
  28. M. Wadati, K. Konno and Y. H. Ichikawa, J. Phys. Soc. Jpn. 46 (1979), 1965[JPSJ].
    T. Shimizu and M. Wadati, Prog. Theor. Phys. 63 (1980), 808 [PTP]
  29. H. B. Thacker and D. Wilkinson, Phys. Rev. D 19 (1979), 3660[APS].
    D. B. Creamer, H. B. Thacker and D. Wilkinson, Phys. Rev. D 21 (1980), 1523[APS]; Phys. Lett. B 92 (1980), 144[CrossRef].
  30. H. Grosse, Phys. Lett. B 86 (1979), 267[CrossRef].
  31. J. Honerkamp, P. Weber and A. Wiesler, Nucl. Phys. B 152 (1979), 266[CrossRef].
  32. L. D. Faddeev, Steklov Mathematical Institute Preprint P-2-79, Leningrad (1979).

Citing Article(s) :

  1. ERROR : Mag:26, Vol:L1912, Page:
  2. Journal of the Physical Society of Japan 56 (1987) pp. 3432-3435 :
    Electron Pairing in Real Space,Model Pseudo-Spin Hamiltonian, and Ginzburg-Landau Equation for High-Tc Oxide Superconductors
    Shozo Takeno
  3. Journal of the Physical Society of Japan 57 (1988) pp. 2257-2260 :
    Josephson Effect and Critical Current by Fermion Pairing in Real Space and High-Tc Oxide Superconductors
    Shozo Takeno and Kenji Kisoda
  4. Progress of Theoretical Physics Vol. 65 No. 6 (1981) pp. 1844-1857 :
    Stationary Solutions to Nonlinear Partial Differential Equations for the Classical Continuous Isotropic Heisenberg Model
    Shozo Takeno and Shigeo Homma
  5. Progress of Theoretical Physics Vol. 66 No. 5 (1981) pp. 1590-1603 :
    Flowing States and Vortices in the Classical XY Model in an External Field
    Shigeo Homma, Toshizumi Aoki and Shozo Takeno
  6. Progress of Theoretical Physics Vol. 67 No. 5 (1982) pp. 1633-1636 :
    Dynamics of Vortices in Two-Dimensional Spin Fluids
    Shozo Takeno and Shigeo Homma
  7. Progress of Theoretical Physics Vol. 69 No. 3 (1983) pp. 773-789 :
    Dynamics of Vortices in Bose Fluids and Classical Continuous Spin Models
    Shozo Takeno and Shigeo Homma

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

Copyright © Progress of Theoretical Physics 2013 All rights reserved.