  We present first calculations of critical spectral functions of the
relaxational Models A, B, and C in the Halperin-Hohenberg classification using
a real-time formulation of the functional renormalization group (FRG). We
revisit the prediction by Son and Stephanov that the linear coupling of a
conserved density to the non-conserved order parameter of Model A gives rise to
critical Model-B dynamics. We formulate both 1-loop and 2-loop self-consistent
expansion schemes in the 1PI vertex functions as truncations of the effective
average action suitable for real-time applications, and analyze in detail how
the different critical dynamics are properly incorporated in the framework of
the FRG on the closed-time path. We present results for the corresponding
critical spectral functions, extract the dynamic critical exponents for Models
A, B, and C, in two and three spatial dimensions, respectively, and compare the
resulting values with recent results from the literature.
