The long wavelength diffusion coefficient of a critical fluid confined between two parallel plates separated by a distance L is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion coefficient as \xi^{ -1} for \xi<<L, \xi being the correlation length, would crossover to \L^{ -1} for \xi>>L. We show that this is not strictlytrue. There is a logarthmic scaling violation. We construct a Kawasaki like scaling function that connects the thermodynamic regime to the extreme critical (\xi>>L) regime.
Categories: cond-mat.stat-mech