Nonlinear dynamic renormalization-group analysis above and below the lambda transition in 4He

Abstract

Recent developments in the theory of the dynamics of liquid 4He near the lambda transition are reviewed. A nonlinear renormalization-group treatment is presented which provides a quantitative description of the dynamics in the entire region between noncritical background and criticality. The previous discrepancies between asymptotic scaling theories and various experiments above and below Tλ are explained in terms of crossover effects. This crossover is governed (i) close to Tλ by the effect of the weak-scaling fixed point, and (ii) farther away from Tλ by a strong decrease of the effective dynamic coupling. New results are presented which are based on the complete flow equations for model F in two-loop order. They tentatively confirm the conclusions of an earlier analysis based on model E and invalidate part of a recent analysis treating model F in an unsystematic way. Excellent agreement is found with new accurate measurements of second-sound damping over four decades in relative temperature.