Abstract
The critical dynamics of liquid helium are studied by means of renormalized field theory on the basis of the symmetric planar-spin model of Halperin, Hohenberg, and Siggia. The stability problem of the dynamic fixed point is discussed in detail. Two-loop results suggest, but do not establish, the stability of the dynamic scaling fixed point. The previously found small fixed point valuew *~O(0.15) is tentatively confirmed which implies a small ratio of relaxation rates of the order parameter and the entropy. The ensuing dynamic transient exponents are calculated. The density correlation function is determined toO(ε=4−d) at and aboveT λ. Its properties in the casew *≪1 provide quantitative support for the recently proposed explanation of the discrepancy between theory and light scattering experiments. A small value ofw * implies pronounced peaks of the frequency spectrum at finite frequencies at and aboveT λ. It also suppresses the temperature dependence of finite-frequency properties over an enlarged critical region as found in light scattering measurements. The quantitative relation between the value ofw *>0 and observable properties of the frequency spectrum is computed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Hohenberg, P.C., Halperin, B.I.: Rev. Mod. Phys.49, 435 (1977)
Halperin, B.I., Hohenberg, P.C., Siggia, E.D.: Phys. Rev. B13, 1299 (1976)
Siggia, E.D.: Phys. Rev. B13, 3218 (1976)
Hohenberg, P.C., Siggia, E.D., Halperin, B.I.: Phys. Rev. B14, 2865 (1976)
Ferrell, R.A., Menyhárd, N., Schmidt, H., Schwabl, F., Szépfalusy, P.: Phys. Rev. Lett.18, 891 (1967); Ann. Phys. (N.Y.)47, 565 (1968)
Halperin, B.I., Hohenberg, P.C.: Phys. Rev.177, 952 (1969)
Winterling, G., Holmes, F.S., Greytak, T.J.: Phys. Rev. Lett.30, 427 (1973) Winterling, G., Miller, J., Greytak, T.J.: Phys. Lett.48 A, 343 (1974)
Vinen, W.F., Palin, C.J., Lumley, J.M., Hurd, D.L., Vaughn, J.M.: Low Temperature Physics, LT-14, edited by M. Krusius and M. Vuorio, Vol. I, p. 191. Amsterdam: North-Holland 1975
Tarvin, J.A., Vidal, F., Greytak, T.J.: Phys. Rev. B15, 4193 (1977)
Tyson, J.A.: Phys. Rev. Lett.21, 1235 (1968)
Ahlers, G.: Phys. Rev. Lett.21, 1159 (1968); in Proceedings of the Twelfth International Conference on Low Temperature Physics, edited by E. Kanda, p. 21. Tokyo: Keigaku 1971
Ahlers, G. In: The Physics of Liquid and Solid Helium, edited by K.H. Benneman and J.B. Ketterson, Vol. 1, Chap. II. New York: Wiley 1976
DeDominicis, C., Peliti, L.: Phys. Rev. Lett.38, 505 (1977)
DeDominicis, C., Peliti, L.: Phys. Rev. B18, 353 (1978)
The existence of a fixed point withw *=0 was first noticed in the context of a planar (n=2) spin model within a first-orderε-calculation by Gunton, J.D., Kawasaki, K.: Progr. Theor. Phys.56, 61 (1976), in which case this fixed point is unstable
Dohm, V., Ferrell, R.A.: Phys. Lett.67 A, 387 (1978)
Dohm, V.: Z. Physik B31, 327 (1978)
Ferrell, R.A., Dohm, V., Bhattacharjee, J.K.: University of Maryland Technical Report#79-003 (July 1978), and Phys. Rev. Lett.41, 1818 (1978)
Ferrell, R.A., Bhattacharjee, J.K.: University of Maryland Technical Report#78-080 (July 1978), submitted to Ann. Phys.
Janssen, H.K.: Z. Physik B23, 377 (1976)
DeDominicis, C.: J. Phys. (Paris)37, Colloque C-247 (1976)
Bausch, R., Janssen, H.K., Wagner, H.: Z. Physik B24, 113 (1976)
Janssen, H.K.: Z. Physik B26, 187 (1977)
Sasvári, L., Schwabl, F., Szépfalusy, P.: Physica81 A, 108 (1975)
Sasvári, L., Szépfalusy, P.: Physica87 A, 1 (1977)
Martin, P.C., Siggia, E.D., Rose, H.A.: Phys. Rev. A8, 423 (1973)
Brézin, E., Le Guillou, J.C., Zinn-Justin, J. In: Phase Transitions and Critical Phenomena, edited by Domb, C., Green, M.S., Vol. 6. New York: Academic 1976
Dohm, V., Janssen, H.K.: Phys. Rev. Lett.39, 946 (1977); J. Appl. Phys.49, 1347 (1978); and Renormalized Field Theory of Bicritical Dynamics, manuscript in preparation
t'Hooft, G., Veltman,M.: Nucl. Phys. B44, 189 (1972)
Halperin, B.I., Hohenberg, P.C., Ma, S.-K.: Phys. Rev. B10, 139 (1974) and13, 4119 (1976) Brézin, E., De Dominicis, C.: Phys. Rev. B12, 4954 (1975) Murata, K.K.: Phys. Rev. B13, 2028 (1976)
Wegner, F.: Z. Physik218, 265 (1969)
Freedman, R., Mazenko, G.F.: Phys. Rev. Lett.34, 1575 (1975); Phys. Rev. B13, 4967 (1976)
Wegner, F.: Z. Physik216, 433 (1968)
Hubbard, J.: J. Phys. C4, 53 (1971)
Dohm, V.: Sol. State Comm.20, 657 (1976). Equation (23) contains a misprint. It should readF(x)=−1/8ln(i x)+P(x −1/2). The normalization point NP in Eq.(16) should beq=0,ω=λµ 4
See however Nolan, M.J., Mazenko, G.F.: Phys. Rev. B15, 4471 (1977) The results of this work disagree qualitatively with those of Ref.37–39, although essentially the same approximation (one-loop approximation) was used. This discrepancy is as yet unresolved. For experimental results see e.g. Dietrich, O.W., Als-Nielsen, J., Passell, L.: Phys. Rev. B14, 4923 (1976), Fig. 10
Author information
Authors and Affiliations
Additional information
Work supported in part by the U.S. National Science Foundation under Grants No. DMR-76-82345 and DMR-76-81185.
Rights and permissions
About this article
Cite this article
Dohm, V. Density correlation function and dynamic transient exponents for liquid helium at and aboveT λ . Z Physik B 33, 79–95 (1979). https://doi.org/10.1007/BF01325816
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01325816