Skip to main content
SpringerLink
Log in

Universal amplitudes for critical surface scattering

  • Published:
Zeitschrift für Physik B Condensed Matter

Abstract

Scattering of x-rays or neutrons at grazing angles is studied for semi-infinite systems which exhibit a second order phase-transition in the bulk. We present the results of a calculation to order ɛ2 (ind=4-ε dimensions) of the amplitudes of leading and next-to-leading terms in the angular dependence and in the temperatur dependence (forT>T c) of the scattering cross-section. The results are discussed for the three-dimensional Ising case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dietrich, S., Wagner, H.: Phys. Rev. Lett.51, 1496 (1983); Z. Phys. B-Condensed Matter56, 203 (1984); Z. Phys. B-Condensed Matter59, 35 (1985)

    Google Scholar 

  2. Dietrich, S.: Conference proceedings of the International Conference on Magnetism, San Francisco, 26.–30. August 1985, J. Magn. Magn. Mater. (to be published)

  3. For a recent review and an extensive list of references see: Binder, K.: Critical behaviour at surfaces. In: Phase transitions and critical phenomena. Domb, C., Lebowitz, J.L. (eds.), Vol. 8. London: Academic Press 1983

    Google Scholar 

  4. For a review of the more theoretical aspects of phase transitions in semi-infinite systems see: Diehl, H.W.: J. Appl. Phys.53, 7914 (1982); manuscript in preparation

    Google Scholar 

  5. Gompper, G.: Z. Phys. B-Condensed Matter56, 217 (1984) There are some misprints in this work which have to be corrected: ϕ(r l ,z=0) in Eq. (3.6) has to be replaced by 366-1 in Eq. (6.7) has to be replaced by 366-2, and 366-3 in Eq. (6.8) has to be replaced by 366-4

    Google Scholar 

  6. Eisenriegler, E.: J. Chem. Phys.81, 4666 (1984); J. Chem. Phys.82, 1032 (1985)

    Google Scholar 

  7. Goldschmidt, Y.Y., Jasnow, D.: Phys. Rev. B29, 3990 (1984)

    Google Scholar 

  8. Diehl, H.W., Gompper, G., Speth, W.: Phys. Rev. B31, 5841 (1985)

    Google Scholar 

  9. Wilson, C.A.: J. Phys. C13, 925 (1980)

    Google Scholar 

  10. Leibler, S., Peliti, L.: J. Phys. C30, L 403 (1982)

    Google Scholar 

  11. Rudnick, J., Jasnow, D.: Phys. Rev. Lett.48, 1059 (1982)

    Google Scholar 

  12. Brezin, E., Leibler, S.: Phys. Rev. B27, 594 (1983)

    Google Scholar 

  13. Diehl, H.W., Dietrich, S.: Z. Phys. B-Condensed Matter50, 117 (1983)

    Google Scholar 

  14. Goldschmidt, Y.Y.: Phys. Rev. B28, 4052 (1983)

    Google Scholar 

  15. Nemirovsky, A.M., Freed, K.F.: Phys. Rev. B31, 3161 (1985)

    Google Scholar 

  16. Amit, D.J.: Field theory, the renormalization group, and critical phenomena. New York: McGraw-Hill 1978

    Google Scholar 

  17. Diehl, H.W., Dietrich, S.: Phys. Lett.80A, 408 (1980); Z. Phys. B-Condensed Matter42, 65 (1981)

    Google Scholar 

  18. Cardy, J.L.: Nucl. Phys. B240, [FS 12], 514 (1984)

    Google Scholar 

  19. Gompper, G., Wagner, H.: Z. Phys. B-Condensed Matter59, 193 (1985)

    Google Scholar 

  20. Hearn, C.A.: Reduce 2 User's manual, Report UCP-19, University of Utah (1973)

Download references

Author information

Authors and Affiliations

  1. Sektion Physik der Universität München, Theresienstrasse 37, D-8000, München 2, Federal Republic of Germany

    G. Gompper

Authors
  1. G. Gompper
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by Bundesministerium für Forschung und Technologie

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gompper, G. Universal amplitudes for critical surface scattering. Z. Physik B - Condensed Matter 62, 357–366 (1986). https://doi.org/10.1007/BF01313459

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01313459

Keywords

Search

Navigation