Scaling laws for random walks in long-range correlated disordered media

Abstract

We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the distance as a power law, r-a, generated with the improved Fourier 1ltering method. To characterize this type of disorder, we determine the percolation threshold pc by investigating cluster-wrapping probabilities. At pc, we estimate the (sub-diffusive) walk dimension dw for different correlation exponents a. Above pc, our results suggest a normal random walk behavior for weak correlations, whereas anomalous diffusion cannot be ruled out in the strongly correlated case, i.e., for small a.