Nonasymptotic critical dynamics near the superfluid transition in4He
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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−Tλ)/Tλ. 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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