Scaling of the spanning threshold in gradient percolation

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Lincoln Paterson

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.

References

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