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 filtering method. To characterize this type of disorder, we determine the percolation threshold p_c by investigating cluster-wrapping probabilities. At p_c, we estimate the (sub-diffusive) walk dimension d_w for different correlation exponents a. Above p_c, 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.

Keywords

• long-range correlated disorder
• critical percolation clusters
• random walks
• exact enumerations
• scaling laws