Long range correlations for stochastic lattice gases in a non-equilibrium steady state

The author considers a system with a single locally-conserved field ( identical to density) in a slab geometry with different densities maintained at the two surfaces of the slab. On the basis of fluctuating hydrodynamics, he shows that the static density-density correlations are long ranged and decay as -1/ mod x-y mod d-2 for dimension d>or=3 over distances small compared to the size of the slab. This effect vanishes to first order in the density difference. As a particle model he investigates a stochastic lattice gas with Kawasaki dynamics. He establishes the connection to fluctuating hydrodynamics. In the case of hard core interaction only he proves the validity of fluctuating hydrodynamics and obtain, presumably model dependent, corrections.