Universal scaling of transport coefficients near the liquid-gas critical point

We employ a novel real-time formulation of the functional renormalization group (FRG) to compute universal scaling functions of the thermal diffusivity and the shear viscosity in the vicinity of the liquid-gas critical point, i.e., for the dynamic universality class of Model H from the Halperin-Hohenberg classification. We map out the universal dependence of the transport coefficients on temperature, external magnetic field, and wavenumber, and provide a detailed comparison with the Kawasaki approximation, which is here obtained from a perturbative one-loop approximation to our real-time FRG flow. In contrast to the Kawasaki approximation, the non-perturbative scaling functions from the full real-time FRG flow show a mild dependence on the thermodynamic path towards the critical point. We further compare our FRG results for the universal wavenumber and temperature dependence of the thermal diffusivity with experimental data from critical fluids.