Journal of Statistical Physics

, Volume 58, Issue 3–4, pp 503–510 | Cite as

Universal incommensurate structures

  • A. E. Jacobs
  • David Mukamel


Certain phase transitions in quasiperiodic systems are characterized byuniversal structures. In these cases the functional form of the order parameter corresponding to the modulated phase,P(r), is determined by the symmetry properties of the system and is independent of the details of the associated Landau-Ginzburg model. Here we consider a simple one-dimensionalXY-like model corresponding to this type of phase transition. The universal modulated structure of this model is calculated numerically at various points along the critical line.

Key words

Universal structures incommensurate systems phase transitions instabilities 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    I. E. Dzyaloshinskii,Zh. Eksp. Teor. Fiz. 46:1420 (1964). [Soviet Phys. JETP 19:960 (1964)]; O. W. Dietrich and J. Als-Nielsen,Phys. Rev. 162:315 (1967); W. C. Koehler,J. Appl. Phys. 36:1078 (1965).Google Scholar
  2. 2.
    M. S. Dresselhaus and G. Dresselhaus,Adv. Phys. 30:139 (1981).Google Scholar
  3. 3.
    A. J. Berlinsky,Rep. Prog. Phys. 42:1243 (1979); G. Grüner,Commun. Solid State Phys. 10:183 (1983).Google Scholar
  4. 4.
    D. Shechtman, I. Blech, D. Gratias, and J. W. Cahn,Phys. Rev. Lett. 53:1951 (1984); L. Bendersky,Phys. Rev. Lett. 55:1461 (1985).Google Scholar
  5. 5.
    P. G. de Gennes, inFluctuations, Instabilities and Phase Transitions, T. Riste, ed. (Plenum Press, New York, 1975).Google Scholar
  6. 6.
    B. Schaub and D. Mukamel,J. Phys. C 16:L225 (1983);Phys. Rev. B 32:6385 (1985).Google Scholar
  7. 7.
    J. W. Felix, D. Mukamel, and R. M. Hornreich,Phys. Rev. Lett. 57:2180 (1986).Google Scholar
  8. 8.
    A. Michelson, Ph. D. thesis, Technion-Israel Institute of Technology (1977), unpublished; T. A. Aslanyan and A. P. Levanyuk,Fiz. Tverd. Tela 20:804 (1978) [Sov. Phys. Solid State 20:466 (1978)].Google Scholar
  9. 9.
    S. Alexander, R. M. Hornreich, and S. Shtrikman, inSymmetries and Broken Symmetries in Condensed Matter Physics, N. Boccara, ed. (Institut pour le Developpement de la Science, l'Education, et la Technologie, Paris, 1981), p. 379.Google Scholar
  10. 10.
    A. L. Korzenevskii,Zh. Eksp. Teor. Fiz. 81:1071 (1981) [Sov. Phys. JETP 54:568 (1981)].Google Scholar
  11. 11.
    D. Blankschtein, E. Domany, and R. M. Hornreich,Phys. Rev. Lett. 49:1716 (1982); D. Blankschtein and R. M. Hornreich,Phys. Rev. B 32:3214 (1985).Google Scholar
  12. 12.
    J. W. Felix and D. M. Hatch,Phys. Rev. Lett. 53:2425 (1984);Jpn. J. Appl. Phys. (Suppl.)24(2):176 (1985).Google Scholar
  13. 13.
    D. Mukamel and M. B. Walker,Phys. Rev. Lett. 58:2559 (1987).Google Scholar
  14. 14.
    O. Biham, D. Mukamel, J. Toner, and X. Zhu,Phys. Rev. Lett. 59:2439 (1987).Google Scholar
  15. 15.
    G. Van Tendeloo, J. Van Landuyt, and S. Amelinckx,Phys. Stat. Sol. A 30:K11 (1975);33:723 (1976); K. Gouhara and N. Kato,J. Phys. Soc. Jpn. 53:2177 (1984);54:1868, 1882 (1985); G. Dolino, J. P. Bachheimer, B. Berge, C. M. E. Zeyen, G. Van Tendeloo, J. Van Landuyt, and S. Amelinckx,J. Phys. (Paris)45:901 (1984).Google Scholar
  16. 16.
    T. A. Aslanyan and A. P. Levanyuk,Solid State Commun. 31:547 (1979); T. A. Aslanyan, A. P. Levanyuk, M. Vallade, and J. Lajzerowicz,J. Phys. C 16:6705 (1985).Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • A. E. Jacobs
    • 1
  • David Mukamel
    • 2
  1. 1.Department of Physics and Scarborough CollegeUniversity of TorontoTorontoCanada
  2. 2.Department of PhysicsWeizmann Institute of ScienceRehovotIsrael

Personalised recommendations