DEEPAK DHAR

Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

Email: ddhar@theory.tifr.res.in

Abstract.

This article reviews some effects of disorder in  percolation systems 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 singularities in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biased 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.

Keywords:  Percolation; lattice animals; biased diffusion; Griffiths singularity.

Pacs Nos.  64.60.Ak; 05.50.+q; 05.40.Fb; 02.50.Ey