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We present first calculations of critical spectral functions of therelaxational Models A, B, and C in the Halperin-Hohenberg classification usinga real-time formulation of the functional renormalization group (FRG). Werevisit the prediction by Son and Stephanov that the linear coupling of aconserved density to the non-conserved order parameter of Model A gives rise tocritical Model-B dynamics. We formulate both 1-loop and 2-loop self-consistentexpansion schemes in the 1PI vertex functions as truncations of the effectiveaverage action suitable for real-time applications, and analyze in detail howthe different critical dynamics are properly incorporated in the framework ofthe FRG on the closed-time path. We present results for the correspondingcritical spectral functions, extract the dynamic critical exponents for ModelsA, B, and C, in two and three spatial dimensions, respectively, and compare theresulting values with recent results from the literature.

Critical dynamics in a real-time formulation of the functional renormalization group