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 $p_{\text{c}}$ by investigating cluster-wrapping probabilities. At $p_{\text{c}}$, we estimate the (sub-diffusive) walk dimension $d_{\text{w}}$ for different correlation exponents $a$. Above $p_{\text{c}}$, 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 $a$.

arXiv comment11 pages, 6 figures

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• Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field
• Temperature scaling analysis of the 3D disordered Ising model with power-law correlated defects