Nonlinear renormalization-group analysis of the thermal conductivity ofHe4forT>~Tλ

The thermal conductivity of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ above the superfluid transition is analyzed using nonlinear renormalization-group recursion relations. Experimental data are presented over a wide temperature range and for various pressures. The dynamic coupling constant far from $T_{\lambda }$ is a small parameter which leads to the possibility of a rigorous test of the theory in a region where perturbation theory is valid. Closer to $T_{\lambda }$ the system crosses over to the scaling regime at a reduced temperature $t_c\approx {10}^{-3\mathrm{}}$, whose smallness results from the weak dynamic coupling far from $T_{\lambda }$. Detailed tests of the theory are presented over the whole temperature range above $T_{\lambda }$, and consistency is found with the asymmetric-spin model ($F$) of Halperin, Hohenberg, and Siggia if corrections are introduced to compensate for truncation errors in the perturbation expansion. The symmetric model ($E$), on the other hand, shows significant deviations from the data even in regions where perturbation theory should hold. The analysis implies a value $d^{*}\lesssim 2.6$ for the dimensionality below which dynamic scaling breaks down. This value is lower than earlier estimates ($d^{*}\approx 3$).