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arXiv · 1703.10368

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

N. Fricke·J. Zierenberg·M. Marenz·F. P. Spitzner·V. Blavatska·W. Janke
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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 $a$.

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N. Fricke, J. Zierenberg, M. Marenz, F. P. Spitzner, V. Blavatska, W. Janke. 2017-03-30. Scaling laws for random walks in long-range correlated disordered media. https://doi.org/10.5488/cmp.20.13004

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