title: Scaling of the spanning threshold in gradient percolation.
abstract: A simple and fast way to apply correlations in percolation simulations is to apply a uniform gradient to the occupancy probabilities. For small networks, exact results are presented here for the spanning thresholds in site percolation with a gradient for networks up to 4×4 in two dimensions and 2×2×2 in three dimensions. Numerical results are provided for larger networks that extrapolate to a linear modification of the threshold proportional to the gradient for moderate values of the gradient.
authors.affiliation: CSIRO, Private Bag 10, Clayton South, Victoria 3169, Australia.
authors.forename: Lincoln
authors.initials: L
authors.lastname: Paterson