Percolation in spatially disordered systems

The coherent-medium approximation is employed to study the percolation processes in a spatially disordered system. Short-range order in the distribution of percolating particles is introduced through the pair distribution function. The effect of a hard-core and a particle interaction on the percolation threshold are studied. The critical percolation density is shown to be an increasing function of the hard-core diameter when the distribution is completely random. When the distribution is not completely random, the critical percolation density can be a decreasing function of the hard-core diameter over a limited range. A density-dependent parameter is introduced in the approximation, in which the critical index of the static diffusion constant at the percolation threshold shows a significant improvement. The dynamic (frequency-dependent) diffusion constant for the percolation model is also obtained in the present approximation.