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Percolation Systems away from the Critical Point

Deepak Dhar
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Abstract

This article reviews some effects of disorder in percolation systems even away from the critical density p_c. For densities below p_c, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singuraties in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biassed diffusion on percolation clusters, trapping in dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near the critical bias field.

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Deepak Dhar. 2001-08-21. Percolation Systems away from the Critical Point. https://doi.org/10.1007/s12043-002-0025-x

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