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A simplified model for the dynamics of the gas-liquid and binary-fluid transitions is studied with the renormalization group. An exact scaling law is found, connecting the exponents for the diverging transport coefficients to static exponents for arbitrary value of the dimensionality d<4. This scaling law had been anticipated by Kadanoff and Swift, and Kawasaki, on the basis of approximate mode-coupling arguments. The "Kawasaki-Stokes" relation between the diffusivity, the shear viscosity, and the correlation length is shown to hold exactly, but with a universal amplitude which differs slightly from its mode-coupling value. Critical exponents for the transport coefficients are evaluated to second order in =4-d, and lead to the prediction of a weak divergence of the shear viscosity (T) (T-{T₂) }^-0. 04 in three dimensions. The weakness of this divergence reflects the existence of a small parameter in the theory, which explains the excellent agreement between Kawasaki's evaluation of the Rayleigh linewidth and experiment. Corrections to the simple Kawasaki theory carried out by various authors are reviewed, and a number of suggestions are made for refining these calculations. The simple model studied in this paper is shown to have the same dynamic properties as real fluids, sufficiently close to the critical point.
Siggia et al. (Mon,) studied this question.