Non-universal behavior of the soft percolation model in three dimensions

We study the soft percolation model in three dimensions, where the connectivity between two sites distributed randomly falls off with distance r as (1−(r/r0)θ)α(θ=1,3) when r0 is a cutoff length. For both models, the diffusivity critical exponent is shown to depend on α, deviating from the universal value for the ordinary process of α=0.