Diffusion on percolation clusters with a bias in topological space: non-universal behaviour

Abstract

We study diffusion on the infinite percolation cluster above the percolation threshold, p>pc, under the influence of a constant bias field E in topological space ('topological bias'). We find that above a critical bias field E,(p) diffusion is anomalous and non-universal: the diffusion exponent df, increases with E as dL= A(p)lln((l - E)/(l+ E))(, while A(p) decreases monotonically with concentration p. This intrinsic anomalous behaviour is supported in a wide range of concentrations p>p, by extensive numerical simulations using the exact enumeration method.