Abstract
We study the crossover regime between the asymptotic critical dynamics and the noncritical background behavior near the superfluid transition of4He. We demonstrate in quantitative detail that our recently introduced nonlinear dynamic renormalizationgroup treatment is indispensable for an appropriate description of the observable critical dynamics. The global features of the flow diagram in the dynamic parameter space of the symmetric planar-spin model of Halperin, Hohenberg and Siggia are discussed. The range of applicability of various local approximations is investigated. The theory is applied to explain the thermal conductivity data of Ahlers in the range 10−6<t<10−2 of relative temperaturet=(T−T λ)/T λ. Special attention is paid to the dependence on the value of the borderline dimensiond * where dynamic scaling breaks down. Excellent agreement with experiment is found only ford *≈3 which is consistent with recent theoretical estimates ofd *. The theory matches well also with the noncritical background behavior. Predictions are made for the range 10−9<t<10−6.
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Ferrell, R.A., Menyhard, N., Schmidt, H., Schwabl, F., Szépfalusy, P.: Phys. Rev. Lett.18 891 (1967); Ann. Phys. (NY)47, 565 (1968)
Halperin, B.I., Hohenberg, P.C.: Phys. Rev. Lett.19, 700 (1967); Phys. Rev.177, 952 (1969)
Halperin, B.I., Hohenberg, P.C., Siggia, E.D.: Phys. Rev. Lett.32, 1289 (1974); Phys. Rev. B13, 1299 (1976); B21 (E), 2044 (1980)
Siggia, E.D.: Phys. Rev. B13, 3218 (1976)
Hohenberg, P.C., Siggia, E.D., Halperin, B.I.: Phys. Rev. B14, 2865 (1976)
Hohenberg, P.C., Halperin, B.I.: Rev. Mod. Phys.49, 435 (1977)
Hohenberg, P.C.: XVIIth International Solvay Congress on Physics, Brussels, Belgium, Nov. 1978 (Proceedings to be published by J. Wiley & Sons)
Dominicis, C. de, Peliti, L.: Phys. Rev. Lett.38, 505 (1977); Phys. Rev. B18, 353 (1978)
Dohm, V., Ferrell, R.A.: Phys. Lett. A67, 387 (1978)
Dohm, V.: Z. Physik B31, 327 (1978)
Ferrell, R.A., Bhattacharjee, J.K.: J. Low Temp. Phys.36, 165 (1979)
Dohm, V.: Z. Physik B33, 79 (1979)
Ferrell, R.A., Dohm, V., Bhattacherjee, J.K.: Phys. Rev. Lett.41, 1818 (1978)
Dohm, V., Folk, R.: Z. Physik B35, 277 (1979)
Ferrell, R.A., Bhattacharjee, J.K.: Phys. Rev. Lett.42, 1638 (1979)
Ferrell, R.A., Bhattacharjee, J.K.: Phys. Rev. B20, 3690 (1979); Proceedings of the International Conference on Dynamic Critical Phenomena. Enz, C.P. (ed.), Berlin, Heidelberg, New York: Springer 1979; and In: Proceedings of the Second US-USSR Symposium on the Scattering of Light by Condensed Matter. Cummins, H. (ed.). New York: Plenum 1979.
Ahlers, G.: In: Proceedings of the Twelfth International Conference on Low Temperature Physics. Kanda, E. (ed.) Tokyo: Keigadu, 1971
Ahlers, G.: In The Physics of Liquid and Solid Helium, Bennemann, K.H., Ketterson, J.B. (eds.), Vol. 1, Chap. II. New York: Wiley 1976
Tarvin, J.A., Vidal, F., Greytak, T.J.: Phys. Rev. B15, 4193 (1977)
Greytak, T.J.: In: Proceedings of the International Conference on Dynamic Critical Phenomena. Enz, C.P. (ed.). Berlin, Heidelber, New York: Springer 1979
dohm, V., Folk, R.: Z. Physik B39, 94 (1980); and Nonlinear Dynamic Remormalization-Group Analysis above and below the Superfluid Transition in4He. March 1980. Phys. Rev. Lett. (submitted to). This work has been presented at the Frühjahrstagung der Deutschen Physikalischen Gesellschaft, Freudenstadt, March 24–28, 1980, and at the VIIth International Seminar on Phase Transitions and Critical Phenomena MECO, Budapest, March 31–April 2, 1980
Ahlers, G.: Phys. Rev. Lett.43, 1417 (1979)
Hohenberg, P.C., Halperin, B.I., Nelson, D.R.: preprint (April 1980)
Dohm, V., Folk, R.: manuscript in preparation
Bausch, R., Janssen, H.K., Wagner, H.: Z. Physik B24, 113 (1976)
See also the reviews by: Janssen, H.K. and by: Peliti, L.: In: Proceedings of the International Conference on Dynamic Critical Phenomena, Enz, C.P. (ed.). Berlin, Heidelber, New York: Springer 1979
Ahlers, G.: Rev. Mod. Phys.52, 489 (1980)
Hohenberg, P.C.: private communication
Ahlers, G.: Talk presented at the Institut für Festkörperforschung der KFA Jülich (June 1980)
Riedel, E.K., Wegner, F.J.: Phys. Rev. B9, 294 (1974)
Nicoll, J.F., Chang, T.S., Stanley, H.E.: Phys. Rev. Lett.32, 1446 (1974); Phys. Rev. B12, 458 (1975)
Nelson, D.R.: Phys. Rev. B11, 3504 (1975)
Nelson, D.R., Rudnick, J.: Phys. Rev. Lett.35, 178 (1975)
Rudnick, J., Nelson, D.R.: Phys. Rev. B13, 2208 (1976)
Kosterlitz, J.M.: J. Phys. C9, 497 (1976)
Nelson, D.R., Domany, E.: Phys. Rev. B13, 236 (1976)
Horner, H.: Z. Physik B23, 183 (1976)
Domany, E., Nelson, D.R., Fisher, M.E.: Phys. Rev. B15, 3493 (1977)
Amit, D.J., Goldschmidt, Y.Y.: Ann. Phys. (N.Y.)114, 356 (1978)
Nattermann, T.: J. Phys. C9, 3337 (1976)
Lawrie, I.D.: J. Phys. A10, 1557 (1977)
Nattermann, T., Trimper, S.: J. Phys. C9, 2589 (1976)
Bruce, A.D., Kosterlitz, J.M., Nelson, D.R.: J. Phys. C9, 825 (1976)
Bruce, A.D.: J. Phys. C10, 419 (1977)
Balian, D., Love, A.: J. Phys. C10, 3633 (1977)
Santos, M.A.: J. Phys. C13, 1205 (1980)
Liebmann, R., Schaub, B., Schuster, H.G.: Z. Physik B37, 69 (1980)
Aharony, A.: In: Phase Transitions and Critical Phenomena. Domb, C., Green, M.S. (eds.), Vol. 6. New York: Academic Press 1976
Siggia, E.D., Nelson, D.R.: Phys. Rev. B15, 1427 (1977)
Siggia, E.D.: Phys. Rev. B15, 2830 (1977)
Sasvari, L., Schwabl, F., Szépfalusy, P.: Physica A81, 108 (1975)
Sasvari, L., Szépfalusy, P.: Physica A87, 1 (1977)
Janssen, H.K.: Z. Physik B26, 187 (1977)
Gunton, J.D., Kawasaki, K.: Prog. Theor. Phys.56, 61 (1976)
Janssen, H.K.: unpublished manuscript (1978)
Nelson, D.R.: Phys. Rev. B14, 1123 (1976)
Fisher, M.E., Aharony, A.: Phys. Rev. B10, 2818 (1974)
For a given initial condition at somet 0, the crossover functionR effλ (t) computed within renormalized theory should also be independent of the renormalization scheme employed, at least in principle within an exact calculation. We thank E. Brézin and P.C. Hohenberg for a useful discussion on these points
Ahlers, G.: Phys. Rev. A3, 696 (1971)
Ahlers, G.: Phys. Rev. A8, 530 (1973)
Hohenberg, P.C., Aharony, A., Halperin, B.I., Siggia, E.D.: Phys. Rev. B13, 2986 (1976)
We wish to thank G. Ahlers for sending us a negative of the original Fig. 6 of [16]
See e.g. Fig. 4 of Fairbank, W.M.: In: Proceedings of the International School of Physics “Enrico Fermi”. Course XXI, edited by G. Careri (Academic Press, New York, 1963), p. 293
Hill, R.W., Lounnasmaa, O.V.: Phil. Mag.2, 143 (1957)
Bowers, R.: Proc. Phys. Soc. (London), Sect. A65, 511 (1952)
Kerrisk, J.F., Keller, W.E.: Phys. Rev.177, 341 (1969)
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Dohm, V., Folk, R. Nonasymptotic critical dynamics near the superfluid transition in4He. Z. Physik B - Condensed Matter 40, 79–93 (1980). https://doi.org/10.1007/BF01295074
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DOI: https://doi.org/10.1007/BF01295074