Diffusion on percolation lattices: The labyrinthine ant

Publisher Website
Google Scholar
Abstract
In a recent conjecture, de Gennes has suggested that the parameters of a random walk on a percolation lattice (an ant in a labyrinth) should disclose information on the transport properties, especially the conductivity, of a percolation system in the critical region. By scaling arguments, we infer a numer of linear relations between several exponents of the random walk and the critical exponents n μ, β, ν – of the percolation problem. We report on Monte‐Carlo calculations of such random walks, on s i t e lattices above the threshold p c, in two and three dimensions. We infer μ=1.72±0.03 for a simple cubic lattice and μ=0.99±0.02 for two‐dimensional lattices; while the latter agrees with some recent predictions, we think here the critical region may be masked by size effects.

This publication has 0 references indexed in Scilit: