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

Abstract

Recent developments in the theory of the dynamics of liquid 4 He 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 T λ are explained in terms of crossover effects. This crossover is governed (i) close to T λ by the effect of the weak-scaling fixed point, and (ii) farther away from T λ 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.