Transport properties of stochastic fluids

We study heat conduction and momentum transport in the context of stochastic fluid dynamics. We consider a fluid described by model H in the classification of Hohenberg and Halperin. We study both non-critical and critical fluids, and we investigate transport properties in two as well as three dimensions. Our results are based on numerical simulations of model H using a Metropolis algorithm, and we employ Kubo relations to extract transport coefficients. We observe the expected logarithmic divergence of the shear viscosity in a two-dimensional non-critical fluid. At a critical point, we find that the transport coefficients exhibit power-law scaling with the system size $L$. The strongest divergence is seen for the thermal conductivity $\kappa$ in two dimensions. We find $\kappa\sim L^{x_\kappa}$ with $x_\kappa=1.6\pm 0.1$. The divergence is weaker in three dimensions, $x_\kappa=1.25 \pm 0.3$, and the scaling exponent for the shear viscosity, $x_\eta$, is significantly smaller than $x_\kappa$ in both two and three dimensions.