Zeitschrift für Physik B Condensed Matter

, Volume 24, Issue 1, pp 113–127 | Cite as

Renormalized field theory of critical dynamics

  • R. Bausch
  • H. K. Janssen
  • H. Wagner
Article

Abstract

We formulate a Gell'Mann-Low-type renormalization group approach to the critical dynamics of stochastic models described by Langevin or Fokker-Planck equations including mode-coupling terms.

Dynamical correlation and response functions are expressed in terms of path integrals, which are investigated by well-known methods of renormalized perturbation theory.

Dynamical scaling laws and relations between static and dynamic critical exponents are derived. The leading temperature-dependence of correlation and response functions is obtained from the Kadanoff-Wilson short-distance expansion. We also consider corrections to dynamic scaling which are due to a finite lattice constant.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Halperin, B.I., Hohenberg, P.C., Ma, S.: Phys. Rev. Lett.29, 1548 (1972); Phys. Rev. B10, 139 (1974)Google Scholar
  2. 2.
    Halperin, B.I., Hohenberg, P.C., Siggia, E.D.: Phys. Rev. Lett.32, 1289 (1974), PreprintGoogle Scholar
  3. 3.
    Ma, S., Mazenko, G.F.: Phys. Rev. Lett.33, 1384 (1974); Phys. Rev. B11, 4077 (1975)Google Scholar
  4. 4.
    Freedman, R., Mazenko, G.F.: Phys. Rev. Lett.34, 1575 (1975)Google Scholar
  5. 5.
    Kuramoto, Y.: Progr. Theor. Phys.51, 1712 (1974)Google Scholar
  6. 6.
    Kawasaki, K., Gunton, J.: Preprint (1975)Google Scholar
  7. 7.
    Kawasaki, K.: Preprint (1975)Google Scholar
  8. 8.
    Halperin, B.I.: Theory of Dynamic Critical Properties, Talk given at the International Conference on Statistical Physics, Budapest 25.–29. Aug. 1975 Further references are listed in References 8 and 14Google Scholar
  9. 9.
    Schroer, B.: Phys. Rev. B8, 4200 (1973)Google Scholar
  10. 10.
    Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: Phys. Rev. D8, 434, D8, 2418 (1973)Google Scholar
  11. 11.
    Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: Field Theoretical Approach to Critical Phenomena. To be published in Vol. VI of “Phase Transitions and Critical Phenomena”, edited by C. Domb and M.S. GreenGoogle Scholar
  12. 12.
    Wilson, K.G.: Phys. Rev.179, 1499 (1969) Kadanoff, L.: Phys. Rev. Lett.23, 1430 (1969) Symanzik, K.: Comm. Math. Phys.23, 49 (1971) Further references may be found in [11]Google Scholar
  13. 13.
    De Dominicis, C.: Saclay preprint DPh-T/74/110Google Scholar
  14. 14.
    De Dominicis, C., Brézin, E., Zinn-Justin, J.: Phys. Rev. B12, 4945 (1975)Google Scholar
  15. 15.
    Brézin, E., De Dominicis, C.: Phys. Rev. B12, 4954 (1975)Google Scholar
  16. 16.
    Graham, R.: Springer Tracts in Modern Physics66. Berlin-Heidelberg-New York: Springer 1973Google Scholar
  17. 17.
    Yahata, H.: Progr. Theor. Phys.51, 2003 (1974); Progr. Theor. Phys.52, 871 (1974)Google Scholar
  18. 18.
    Janssen, H.K.: Z. Physik B23, 377 (1976)Google Scholar
  19. 19.
    Martin, P.C., Siggia, E.D., Rose, H.A.: Phys. Rev. A8, 423 (1973)Google Scholar
  20. 20.
    Zwanzig, R.W.: Phys. Rev.124, 983 (1961)Google Scholar
  21. 21.
    Mori, H.: Progr. Theor. Phys.33, 423 (1965);52, 433 (1974)Google Scholar
  22. 22.
    Kawasaki, K.: J. Phys. A6, 1289 (1973)Google Scholar
  23. 23.
    Wilson, K.G., Kogut, J.B.: Phys. Rep.12C, 75 (1974)Google Scholar
  24. 24.
    Graham, R., Haken, H.: Z. Physik243, 289 (1971)Google Scholar
  25. 25.
    Graham, R., Haken, H.: Z. Physik245, 141 (1971)Google Scholar
  26. 26.
    Deker, U., Haake, F.: Phys. Rev. A11, 2043 (1975)Google Scholar
  27. 27.
    Zinn-Justin, J.: Wilson's Theory of Critical Phenomena and Renormalized Perturbation Theory, Lectures given at the 1973 Cargése Summer School (edited by E. Brézin and J.M. Charap, Gordon and Breach)Google Scholar
  28. 28.
    Brézin, E., Amit, D., Zinn-Justin, J.: Phys. Rev. Lett.32, 151 (1974) Further references may be found in [11]Google Scholar
  29. 29.
    Zimmermann, W.: Lectures on Elementary Particles and Quantum Field Theory, edited by S. Deser et al. Cambridge, Mass.: MIT Press 1971 Callan, C.G.: Phys. Rev. D5, 3202 (1972)Google Scholar
  30. 30.
    Wagner, H.: Physics Lett.33A, 58 (1970)Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • R. Bausch
    • 1
  • H. K. Janssen
    • 1
  • H. Wagner
    • 1
  1. 1.Institut für FestkörperforschungKernforschungsanlage Jülich GmbHJülich 1Federal Republic of Germany

Personalised recommendations