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Critical ultrasound attenuation in isotropic systems

  • Original Contributions
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Zeitschrift für Physik B Condensed Matter

Abstract

Starting with a complete set of coupled Langevin equations for the hydrodynamic variables including the order parameter and the acoustic phonons, the critical sound dispersion relation is derived for models C and F. The final expression for the sound dispersion relation contains a quantity which can be interpreted as a frequency-dependent specific heat depending only on the critical degrees of freedom. The elimination of the phonons from the self-energy is justified in detail. Our microscopic result agrees with the phenomenological formula of Ferrell and Bhattarcharjee only in limiting cases. In general, as for instance for model F, it is more complicated than one could have anticipated on a phenomenological basis. For model C, the scaling function of the critical sound attenuation coefficient is calculated to two-loop order. Finally, it is shown that for model C with more than one order parameter component and model F the sound dispersion relation obtained at the critical point is also valid in the crossover region between the critical point and the coexistence region which is in a critical state due to the Goldstone modes.

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References

  1. Holt, R.M., Fossheim, K.: Phys. Rev. B24, 2680 (1981)

    Google Scholar 

  2. Mueller, P.E., Eden, D.E., Garland, C.W., Williamson, R.C.: Phys. Rev. A6, 2272 (1972)

    Google Scholar 

  3. Suzuki, M., Komatsubara, T.: J. Phys. C15, 4559 (1982)

    Google Scholar 

  4. Ferrell, R.A., Bhattarcharjee, J.K.: Phys. Lett. A86, 109 (1981) ibid88, 77 (1982)

    Google Scholar 

  5. Ferrell, R.A., Bhattarcharjee, J.K.: Phys. Rev. A31, 1788 (1985)

    Google Scholar 

  6. Fixman, M.: J. Chem. Phys.36, 1961 (1962)

    Google Scholar 

  7. Botch, W., Fixman, M.: J. Chem. Phys.42, 199 (1965), see also Kawasaki, K.: Int. J. Magn.1, 171 (1971)

    Google Scholar 

  8. Kawasaki, K., Shiwa, Y.: Physica A113, 27 (1982)

    Google Scholar 

  9. Pankert, J., Dohm, V.: Europhys. Lett.2, 775 (1986)

    Google Scholar 

  10. Ferrell, R.A., Bhattarcharjee, J.K.: Phys. Rev. Lett.44, 408 (1980), Phys. Rev. B23, 2434 (1981); Ferrell, R.A., Mirhasher, B., Bhattarcharjee, J.K.: Phys. Rev. B35, 4662 (1987)

    Google Scholar 

  11. Dengler, R., Schwabl, F.: Z. Phys. B69, 327 (1987)

    Google Scholar 

  12. Dengler, R., Schwabl, F.: Europhys. Lett.4, 1233 (1987)

    Google Scholar 

  13. Pankert, J., Dohm, V.: Phys. Rev. B40, 10842, 10856 (1989)

    Google Scholar 

  14. Schwabl, F., Iro, H.: Ferroelectrics35, 215 (1981); Iro, F., Schwabl, F.: Solid State Commun.46, 205 (1983)

    Google Scholar 

  15. Slonczewski, J.C., Thomas, H.: Phys. Rev. B1, 3599 (1970)

    Google Scholar 

  16. Lawrie, I.D.: J. Phys. A14, 2489 (1981)

    Google Scholar 

  17. Täuber, U.C., Schwabl, F.: Phys. Rev. B46, 3337 (1992)

    Google Scholar 

  18. Schorgg, A.M., Schwabl, F.: Phys. Lett. A168, 437 (1992)

    Google Scholar 

  19. Hohenberg, P.C., Halperin, B.I.: Rev. Mod. Phys.49, 435 (1977)

    Google Scholar 

  20. Dengler, R.: Private communication. The model (2.1) can also be viewed as a special case of modelF with phonons introduced in [13]

  21. Landau, L., Lifschitz, E.M.: Course of theoretical physics. Vol. 5: Statistical physics. Chap. XII. Oxford: Pergamon Press 1969

    Google Scholar 

  22. Halperin, B.I., Hohenberg, P.C., Ma, S.: Phys. Rev. B10, 129 (1974)

    Google Scholar 

  23. Bausch, R., Janssen, H.K., Wagner, H.: Z. Phys. B24, 113 (1976)

    Google Scholar 

  24. De Dominicis, C., Peliti, L.: Phys. Rev. B18, 353 (1978)

    Google Scholar 

  25. Wallace, D.J.: In Phase transitions and critical phenomena. Vol. 6, p. 352. Domb, C., Green, M.S. (eds.). London: Academic Press 1976

    Google Scholar 

  26. t'Hooft, G., Veltman, M.: Nucl. Phys. B44, 189 (1972)

    Google Scholar 

  27. Lawrie, I.D.: J. Phys. A9, 961 (1976)

    Google Scholar 

  28. Dohm, V.: Phys. Rev. B29, 1497 (1984)

    Google Scholar 

  29. Dzyaloshinskii, I.E., Volovick, G.E.: Ann. Phys. (N.Y.)125, 67 (1980)

    Google Scholar 

  30. Brezin, E., Zinn-Justin, J.: Phys. Rev. B14, 3110 (1976)

    Google Scholar 

  31. Cummins, H.Z.: Phys. Rep.185, 211 (1990)

    Google Scholar 

  32. Schorgg, A.M., Schwabl, F.: Phys. Rev. B46, 8828 (1992)

    Google Scholar 

  33. Pawlak, A.: J. Phys. C1, 7989 (1989)

    Google Scholar 

  34. Bergman, D.J., Halperin, B.I.: Phys. Rev. B13, 2145 (1976)

    Google Scholar 

  35. de Moura, M.A., Lubensky, T.C., Imry, Y., Aharony, A.: Phys. Rev. B13, 2176 (1976)

    Google Scholar 

  36. Schatz-Drossel, B.: Diploma Thesis, TU München 1989

  37. Nattermann, T.: J. Phys. C9, 3337 (1976); J. Phys. A10, 1757 (1977)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Physik-Department, Technische Universität München, James-Franck-Strasse, W-8046, Garching, Germany

    B. Drossel & F. Schwabl

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  1. B. Drossel
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  2. F. Schwabl
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Drossel, B., Schwabl, F. Critical ultrasound attenuation in isotropic systems. Z. Physik B - Condensed Matter 91, 93–111 (1993). https://doi.org/10.1007/BF01316712

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  • DOI: https://doi.org/10.1007/BF01316712

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