Renormalization-group calculation of the superfluid/normal-fluid interface of liquid 4He in gravity near Tλ

The superfluid/normal-fluid interface of liquid He-4 is investigated in gravity on earth where a small heat current Q flows vertically upward or downward. We present a local space- and time-dependent renormalization-group (RG) calculation based on model F, which describes the dynamic critical effects for temperatures T near the superfluid transition T-lambda. The model-F equations are rewritten in a dimensionless renormalized form and solved numerically as partial differential equations. Perturbative corrections are included for the spatially inhomogeneous system within a self-consistent one-loop approximation. The RG flow parameter is determined locally as a function of space and time by a constraint equation, which is solved by a Newton iteration. As a result we obtain the temperature profile of the interface. Furthermore, we calculate the average order parameter <psi >, the correlation length xi, the specific heat C-Q, and the thermal resistivity rho(T) where we observe a rounding of the critical singularity by the gravity and the heat current. We compare the thermal resistivity with an experiment and find good qualitative agreement. Moreover, we discuss our previous approach for larger heat currents and the self-organized critical state and show that our theory agrees with recent experiments in this latter regime.