Abstract
It is suggested that pulse soliton solutions for the classical, continuum, isotropic, ferromagnetic Heisenberg chain in a magnetic field continuously deform to sine Gordon breather solutions as anisotropy is increased to an extremeXY limit (theXY plane containing the applied field). The relevance of this observation for applications to magnetic chains such as CsNiF3 is emphasized, and comparisons with the zero-field limit are noted.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Long, K.A., Bishop, A.R.: J. Phys. A12, 1325 (1979); see also Kosevich, A.M., Ivanov, B.A., Kovalev, A.S.: Fiz. Niz. Temperatur3, 906 (1977). (We thank Dr. E.K. Sklyanin for bringing this work to our attention)
Takhtajan, L.A.: Phys. Lett.64A, 235 (1977)
e.g. Bullough, R.K., Dodd, R.K.. In: Solitons and Condensed Matter Physics. Bishop, A.R., Schneider, T. (eds.) Berlin, Heidelberg, New York: Springer 1978
Fogedby, H.C.: J. Phys. A (in press) and preprint (1979). See also Jevicki A., Papanicolaou N.: Annal. Phys.120, 107 (1979)
Dashen, R.F., Hasslacher, B., Neveu, A.: Phys. Rev.D 11, 3424 (1975)
Luther, A.: Phys. Rev.B14, 2153 (1976); and in “Solitons”, Bullough, R.K., Caudrey, P.J. (eds.) Berlin, Heidelberg, New York: Springer (in press)
Faddeev, L.D.: to appear in “Soviet Scientific Reviews”, 1980 (Harwood Academic Publishers, London); Kulish, P.P., Sklyanin, E.K.: Phys. Lett.70A, 461 (1979)
Steiner, M., Villain, J., Windsor, C.G.: Adv. Phys.25, 87 (1976)
Mikeska, H.J.: J. Phys.C11, L29 (1978)
Allroth, E., Mikeska, H.J.: J. Phys.C8, L523 (1975)
Schneider, T., Stoll, E., Jauslin, H.R.: preprint (1979)
e.g. Bishop, A.R.: Solid State Commun.30, 37 (1979)
Kjems, J.K., Steiner, M.: Phys. Rev. Lett.41, 1137 (1978)
Loveluck, J.M., Balcar, E.: Phys. Rev. Lett.42, 1563 (1979)
Loveluck, J.M., Lovesey, S.W.: J. Phys. C (in press)
Currie, J.F., Krumhansl, J.A., Bishop, A.R., Trullinger, S.E.: Phys. Rev. B (1979), in press; Takayama, H., Maki, K.: Phys. Rev. B (1979)
e.g. Belavin, A.A., Polyakov, A.M.: JETP Lett.22, 503 (1975)
Kosterlitz, J.M., Thouless, D.J.: J. Phys.C6, 1181 (1973) Hikami, S., Tsuneto, T.: preprint (1979)
McGurn, A.R., Scalapino, D.J.: Solid State Commun.15, 1463 (1974) Nakamura, K., Sasada, T.: J. Phys. C11, 331 (1978)
Patkós, A., Ruján, P.: Z. PhysikB33, 163 (1979)
e.g. Newell, A.C.: In: Solitons and Condensed Matter Physics. Bishop, A.R., Schneider, T. (eds.) Berlin, Heidelberg, New York: Springer 1978
Kaup, D.J., Newell, A.C.: Proc. R. Soc.361, 413 (1978)
Stoll, E., Schneider, T., Bishop, A.R.: Phys. Rev. Lett.42, 937 (1979)
Zhakarov, V.E., Manakov, S.V. In: Soviet Scientific Reviews. Vol. 1. London: Harwood Academic Publishers 1979 Zhakarov, V.E., Takhtajan, L.A.: Teor. i Mat. Fiz.38, 26 (1979); see also Corones, J.: Phys. Rev.B16, 1763 (1977)
Lakshmanan, M.: Phys. Lett.61A, 53 (1977); Lamb, G.L., Jr.: J. Math. Phys.18, 1654 (1977)
Bethe, H.: Z. Physik71, 205 (1931)
Baxter, R.J.: Ann. Phys.70, 323 (1972)
e.g. Johnson, J.D., Krinsky, S., McCoy, B.M.: Phys. Rev.A8, 2526 (1973); Johnson, J.D., Bonner, J.C.: Phys. Rev. Lett.44, 616 (1980), and private communications
e.g. Lüscher, M.: Nucl. Phys.B117, 475 (1976); Bergknoff, H., Thacker, H.B.: Phys. Rev. Lett.42, 135 (1979); Phys. Rev. D19, 3666 (1979)
Borovik, A.E.: Pisma JETP28, 629 (1978)
Sklyanin, E.K.: private communications (1979)
c.f. numerical evidence for two excitation branches in classical anisotropic Heisenberg: Tjon, J., Wright, J.: Phys. Rev.B15, 3470 (1977)
Villain, J.: J. Phys.C6, L97 (1973); J. Physique (Paris)35, 27 (1974); José, J.V., Sahni, P.S.: Phys. Rev. Lett.43, 78 (1979)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bishop, A.R. Comments on nonlinear excitations in the anisotropic Heisenberg chain. Z Physik B 37, 357–361 (1980). https://doi.org/10.1007/BF01352747
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01352747