Title: Scaling laws for random walks in long-range correlated disordered media
Author(s):

	N. Fricke (Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D–04009 Leipzig, Germany) ,
	J. Zierenberg (Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D–04009 Leipzig, Germany; Bernstein Center for Computational Neuroscience, Am Fassberg 17, D-37077 Göttingen, Germany; Max Planck Institute for Dynamics and Self-Organsization, Am Fassberg 17, D-37077 Göttingen, Germany) ,
	M. Marenz (Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D–04009 Leipzig, Germany) ,
	F.P. Spitzner (Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D–04009 Leipzig, Germany) ,
	V. Blavatska (Institute for Condensed Matter Physics of the National Academy of Sciences of Ukraine, 1 Svientsitskii St., 79011 Lviv, Ukraine) ,
	W. Janke (Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, D–04009 Leipzig, Germany)

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.

Key words: long-range correlated disorder, critical percolation clusters, random walks, exact enumerations, scaling laws
PACS: 05.70.Jk, 64.60.al, 64.60.De

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