Thermal conductivity ofHe4I nearTλfrom vapor pressure to 28 bars: Comparison of experiment and theory

We compare recent thermal-conductivity measurements near the superfluid transition temperature $T_{\lambda }$(P) with recent complete two-loop-order field-theoretical calculations of the renormalization-group recursion relations and of the relation between the conductivity and the dynamic variables of the theory. The comparison involves a numerical integration of the recursion relations, and thus contains certain dynamic transients to all orders. We find excellent agreement over a wide range of pressure and reduced temperature when the complete two-loop theory is used. Neglect of any of a number of ingredients of the theory results in a deterioration of the agreement with experiment. In particular, it is necessary to use the full asymmetric planar spin model (model F) of the dynamics, and to include singular static transients in the theory, in order to obtain a good fit. From our analysis above $T_{\lambda }$(P), and a calculation of the second-sound damping $D_2$ below $T_{\lambda }$(P) based on the symmetric planar spin model (model E), we estimate $D_2$. As in earlier work, we still find small differences between theory and experiment, and attribute them to the use of model E in the derivation of the formula for $D_2$.