Critical Thermal Conductivity ofHe4forT>~Tλ

Nonlinear renormalization-group recursion relations are used to show that the thermal conductivity of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has a crossover between a weak-coupling regime for $t_c\ll t<\mathrm{}1\mathrm{}$ and a scaling regime for $t\ll t_c$, where $t=\frac{(T-T_{\lambda })}{T_{\lambda }}$ and $t_c\approx {10}^{-3\mathrm{}}$. The smallness of $t_c$—an essential feature—is explained by a small bare dynamic coupling constant. The asymmetric spin model ($F$) provides a quantitative fit to experiment, whereas the symmetric model ($E$) is only semiquantitative. The border-line dimension $d^{*}$, below which dynamic scaling breaks down, is shown to satisfy $d^{*}\lesssim 2.54$.