Nonuniversal diffusion exponent for a soft percolation process in three dimensions

The diffusion property of a soft percolation process in three dimensions is studied. The jump rate of a random walker between two sites distributed ra ndomly in space is assumed to fall off with the distance r as w similar to [1- (r/r(0))](alpha) where r(0) is a cutoff length. The diffusion exponent d(w) is determined by a new computational approach using the exact expressi on for mean-square displacement, [r(2)(t)], of a random walker on a single percolation cluster. The diffusion exponent dw is shown to depend on alpha, deviating gradually from the value for alpha = 0.