Abstract
The mean field equations of the simple cubic or tetragonal ANNNI model are studied on finite lattices. Structure combination branching processes are found which allow us to considerably refine previous mean field calculations on the model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Fisher, M.E., Selke, W.: Phys. Rev. Lett.44, 1502 (1980)
For reviews see Bak, P.: Rep. Prog. Phys.45, 587 (1982); Fisher, M.E., Huse, D.A.: Melting, localization and chaos. Kalia, R.K., Vashishta, P. (eds.), p. 259. New York: Elsevier 1982; Selke, W.: In: Modulated structure materials. Tsakalakos, T. (ed.), p. 23. NATO ASI Series: Martinus Nijhoff 1984
Fisher, M.E., Selke, W.: Philos. Transact. R. Soc. London302, 1 (1981)
Uimin, G.V.: J. Stat. Phys.34, 1 (1984); see also Pokrovsky, V.L., Uimin, G.V.: Zh. Eksp. Teor. Fiz.82, 1640 (1982); Smith, J., Yeomans, J.: J. Phys. C16, 5305 (1983); Szpilka, A.M.: J. Phys. (1984)
Selke, W., Fisher, M.E.: Phys. Rev. B20, 257 (1979); J. Magn. Magn. Mater.15–18, 403 (1980)
Kawasaki, T.: J. Phys. Soc. Jpn.52, Suppl. 239 (1983)
von Boehm, J., Bak, P.: Phys. Rev. Lett.42, 122 (1979)
Bak, P., von Boehm, J.: Phys. Rev. B21, 5297 (1980)
Rasmussen, E.B., Knak-Jensen, S.J.: Phys. Rev. B24, 2744 (1981)
Villain, J., Gordon, M.: J. Phys. C13, 3117 (1980)
Bak, P.: Phys. Rev. Lett.46, 791 (1981)
Öttinger, H.C.: J. Phys. A16, 1483 (1983)
Jensen, M.H., Bak, P.: Phys. Rev. B27, 6853 (1983)
Yokoi, C.S.P., Coutinho-Filho, M.D., Salinas, S.R.: Phys. Rev. B24, 4047 (1981); Kaburagi, M., Tonegawa, T., Kanamori, J.: J. Phys. Soc. Japan53, 1971 (1984)
Duxbury, P.M., Selke, W.: J. Phys. A16, L741 (1983)
Yamada, Y., Shibuya, I., Hoshino, S.: J. Phys. Soc. Japan18, 1594 (1963)
Durand, D., Denoyer, F., Lefur, D., Currat, R., Bernhard, L.: J. Phys. (Paris) Lett.44, L207 (1983)
Elliott, R.J.: Phys. Rev.124, 346 (1961)
Selke, W.: J. Phys. C14, L14 (1981)
Frank, F.C., van der Merwe, J.H.: Proc. R. Soc. London Ser. A198, 205 (1949); see also Frenkel, Y., Kontorowa, T.: Zh. Eksp. Teor. Phys.8, 89 (1938)
Aubry, S.: in Soliton and Condensed Matter Physics. Bishop, A.R., Schneider, T. (eds.), p. 264. Berlin, Heidelberg, New York: Springer 1978; Aubry, S.: J. Phys. (Paris)44, 147 (1983)
Redner, S., Stanley, H.E.: Phys. Rev. B16, 4901 (1977); Oitmaa, J.: Preprint
Montambaux, G., Lederer, P.: Preprint; see also Inawashiro, S., Thompson, C.J., Honda, G.: J. Stat. Phys.33, 419 (1983); de Fontaine, D., Kulik, J.: Acta Metallurgica (1984)
Aharony, A., Bak, P.: Phys. Rev. B23, 4770 (1981)
Hornreich, R.M., Luban, M., Shtrikman, S.: Phys. Rev. Lett.35, 1678 (1975)
Böhm, H.: Z. Kristallographie148, 207 (1978); Ishibashi, Y., Shiba, H.: J. Phys. Soc. Jpn.45, 409 (1978); Ehrhardt, K.D., Michel, K.H.: Phys. Rev. Lett.46, 291 (1981); Levanyuk, A.P., Sannikov, D.G.: Sov. Phys. Solid State18, 1122 (1976); Ishibashi, Y., Buchheit, W., Petersson, J.: Solid State Commun.38, 1277 (1981); Michel, K.H.: Phys. Rev. B24, 3998 (1981); for a review on incommensurate structures in ferroelectrics, see Janssen, T.: Preprint
Moudden, A.H., Moncton, D.E., Axe, J.D.: Phys. Rev. Lett.51, 2390 (1983); see also Durand, D., Denoyer, F., Currat, R., Vettier, C.: Preprint (1984)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Selke, W., Duxbury, P.M. The mean field theory of the three-dimensional ANNNI model. Z. Physik B - Condensed Matter 57, 49–58 (1984). https://doi.org/10.1007/BF01679925
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01679925