Contra-universality in percolation with variable strength of connection

Strength of connection between two sites is introduced in a dynamic percolation process in spatially disordered systems, where the jump rate between two sites is assumed to have a power-law dependence on the distance between the sites with a cut-off. With use of the coherent medium approximation and the effective-z method by Odagaki and Lax (1987), it is predicted that the conductivity exponent depends on the power, though the critical percolation density does not, that is, the percolation transition in this model is contra-universal.