Dynamic critical behavior near the superfluid transition in 3He-4He mixtures in two loop order

We calculated in two loop order the field theoretic renormalization group functions taking into account the decomposition of the dynamical vertex functions into the static vertex functions and genuine dynamical parts. The observation of this nonperturbative structure simplifies the theoretical expressions obtained by perturbation theory considerably and makes tractable a complete two loop calculation of the critical dynamics near the superfluid transition of 3He-4He mixtures (model F'). As a result, we obtain various transport coefficients, which govern the nonasymptotic and nonuniversal temperature dependence. We also correct long-standing results for the critical dynamics of the superfluid transition in pure 4He (model F) and for the dynamics of structural or magnetic phase transitions (model C).