Advertisement

Renomarlization group calculations for critical and tricritical dynamics applied to helium

  • L. Peliti
Critical Dynamics of Liquid Helium
Part of the Lecture Notes in Physics book series (LNP, volume 104)

Abstract

Renormalization group calculations for the critical dynamics of liquid Helium and of He3-He4 mixtures are reviewed. The role of different fixed points in determining the asymptotic behaviour is discussed. Emphasis is laid upon ambiguities in extrapolating results of d=4−ε calculations down to d=3. [/ p]

Keywords

Renormalization Group Critical Exponent Stable Fixed Point Critical Dynamic Dynamic Scaling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B.I.Halperin, P.C.Hohenberg, S.K.Ma, Phys.Rev.Lett. 29, 1548 (1972); Phys.Rev. B10, 139 (1974); Phys.Rev. B13, 4119 (1976).CrossRefGoogle Scholar
  2. [2]
    See the review article by P.C.Hohenberg and B.I.Halperin, Rev. Mod.Phys. 49, 435 (1977) and references therein.CrossRefGoogle Scholar
  3. [3]
    B.I.Halperin, P.C.Hohenberg, E.D.Siggia, Phys.Rev.lett. 31, 1289 (1974); Phys.Rev. B13, 1299 (1976).CrossRefGoogle Scholar
  4. [4]
    E.Brézin, C.De Dominicis, Phys.Rev. B12, 4954 (1975).Google Scholar
  5. [5]
    See e.g. P.C.Hohenberg and P.C.Martin, Ann.Phys.(N.Y.), 34, 291 (1965).CrossRefGoogle Scholar
  6. [6]
    B.I.Halperin, P.C.Hohenberg Phys.Rev.188, 898 (1969).CrossRefGoogle Scholar
  7. [7]
    R.A.Ferrell, N.Menyhàrd, H.Schmidt, F.Schwabl, P.Szépfalusy, Phys. Rev.Lett. 18, 891 (1967); Ann.Phys. (N.Y.) 47, 565 (1968).CrossRefGoogle Scholar
  8. [8]
    P.C.Martin, E.D.Siggia, H.A.Rose, Phys.Rev. A8 423 (1973)Google Scholar
  9. [8a]
    C. De Dominicis, J. Phys. (Paris) C1, 247 (1976)Google Scholar
  10. [8b]
    H.K. Janssen, Z. Phys. B23, 377 (1976).Google Scholar
  11. [9]
    R.Bausch, H.K.Janssen, H.Wagner, Z.Physik B24, 113 (1976).Google Scholar
  12. [10]
    C.De Dominicis, L.Peliti, Phys.Rev.Lett.38, 505 (1977); Phys.Rev. B18, 353 (1978).CrossRefGoogle Scholar
  13. [11]
    G.'t Hooft, M.Veltman, Nucl.Phys. B44, 189 (1972); C.G.Bollini, J.J. Giambiagi, Phys.Lett. B40, 566 (1970).CrossRefGoogle Scholar
  14. [12]
    G.Ahlers, in The Physics of Liquid and Solid Helium, K.H.Benneman and J.B.Petterson (Eds.) Part.I, Section 2. New York: Wiley (1976).Google Scholar
  15. [13]
    G.Ahlers, Phys.Rev.Lett.21, 1159 (1968); in Proceedings of the Twelfth International Conference on Low Temperature Physics, E.Kanda (Ed.), p.21 Tokyo: Keigaku (1971).CrossRefGoogle Scholar
  16. [14]
    H.K.Janssen, Z.Physik B26, 187 (1977).Google Scholar
  17. [15]
    V.Dohm, Z.Physik B33, 79 (1979).Google Scholar
  18. [16]
    L.Sasvàri, F.Schwabl, P.Szépfalusy: Physica 81A, 108 (1975).Google Scholar
  19. [17]
    B.I.Halperin, Phys.Rev. B11, 178 (1975).Google Scholar
  20. [18]
    V.Dohm, Z.Physik B31, 327 (1978).Google Scholar
  21. [19]
    R.A.Ferrell,V.Dohm, J.K.Bhattacharjee, Phys.Rev.Lett. 41, 1818 (1978). See also the communication by Ferrel to this Conference.CrossRefGoogle Scholar
  22. [20]
    G.Winterling, F.S.Holmes, T.J.Greytak: Phys.Rev.Lett.30, 427 (1973); G.Winterling, J.Miller, T.J.Greytak: Phys.Lett. 48A, 343 (1974); M.F.Vinen, C.J.Palin, J.M.Lumley, D.L.Hurd, and J.M.Vaughan, in Low Temperature Physics, LT-14, M.Krusius and M.Vuorio (Eds.) Vol.I, p.191, Amsterdam: North-Holland (1975).CrossRefGoogle Scholar
  23. [21]
    P.C.Hohenberg, E.D.Siggia, B.I.Halperin, Phys.Rev.B14, 2865 (1876).Google Scholar
  24. [22]
    E.D.Siggia, D.R.Nelson, Phys.Rev. B15, 1427 (1977)Google Scholar
  25. [23]
    E.D.Siggia, Phys.Rev. B15, 2830 (1977).Google Scholar
  26. [24]
    See e.g. the communication by H.Meyer, this Conference.Google Scholar
  27. [25]
    V.Dohm, H.K.Janssen, Phys.Rev.39, 946 (1977); J.Appl.Phys. 49, 1347 (1978) and to be published.Google Scholar
  28. [26]
    K.K.Murata, Phys.Rev.B12, 4954 (1975).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • L. Peliti
    • 1
  1. 1.GNSM-CNR, Unità di Roma Istituto di FisicaUniversità di CamerionCamerino (MC)Italy

Personalised recommendations