Nonuniversality of diffusion exponents in percolation systems

We study diffusion on the incipient infinite percolation cluster in $d=2$ with a power-law distribution of transition rates P(W)~W^-α, α<1. Using the exact enumeration method we find that the diffusion exponent d̄w(α) sticks at its α=-∞ value for α0. For α>0, d̄w is bounded by ${d}f+{1}{[{(1{-}{α})}_{{ν}}]}{}{d̄}w({α}){}{d̄}w({-}{∞})+{{α}}{[{(1{-}{α})}_{{ν}}}]$. Specifically, for small ${α}$ our numerical results are close to the upper bound, while for larger ${α}$ they are close to the lower bound.