Deviations from dynamic scaling at the superfluid transition in two and three dimensions

The slow approach to dynamic-scaling behavior at the three-dimensional superfluid transition is analyzed using the recursion relations of De Dominicis and Peliti, and Dohm, accurate to second order in $\epsilon =4-d$. The consequences of the prediction that $d=3\mathrm{}$ is close to the limit of stability of the dynamic-scaling fixed point are explored, and it is shown that experimental observations are not much affected if the dynamic-scaling fixed point is actually unstable at $d=3\mathrm{}$. Results are compared with predictions for the $d=2\mathrm{}$ superfluid transition, where dynamic scaling is seriously violated. The behavior in two dimensions is inconsistent with both the weak- and strong-scaling fixed points.