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

Fricke, Zierenberg, Marenz, Spitzner, Blavatska, Janke
2017 Condensed Matter Physics  
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
more » ... 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 $a$.
doi:10.5488/cmp.20.13004 fatcat:kxprmwfg2bedtkz5ksw2hb3rnm