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Scaling of the spanning threshold in gradient percolation
Phys. Rev. E 91, 022116 – Published 12 February, 2015
DOI: https://doi.org/10.1103/PhysRevE.91.022116
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 in two dimensions and 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.
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