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

Abstract

The authors study diffusion on the infinite percolation clusters above the percolation threshold, p>pc, under the influence of a constant bias field E in topological space ('topological bias'). They find that above a critical bias field Ec(p) diffusion is anomalous and non-universal: the diffusion exponent dwl increases with E as dwl=A(p) mod ln((1-E)/(1+E)) mod , while A(p) decreases monotonically with concentration p. This intrinsic anomalous behaviour is supported in a wide range of concentrations p>pc by extensive numerical simulations using the exact enumeration method.