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000840252 1001_ $$0P:(DE-Juel1)136887$$aGrassberger, Peter$$b0$$eCorresponding author
000840252 245__ $$aPercolation in Media with Columnar Disorder
000840252 260__ $$aNew York, NY [u.a.]$$bSpringer Science + Business Media B.V.$$c2017
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000840252 520__ $$aWe study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active (“growth”) sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.
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000840252 7001_ $$0P:(DE-HGF)0$$aHilário, Marcelo R.$$b1
000840252 7001_ $$0P:(DE-HGF)0$$aSidoravicius, Vladas$$b2
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