Efficient measurement of the percolation threshold for fully penetrable discs

We study the percolation threshold for fully penetrable discs by measuring the average location of the frontier for a statistically inhomogeneous distribution of fully penetrable discs. We use two different algorithms to efficiently simulate the frontier, including the continuum analogue of an algorithm previously used for gradient percolation on a square lattice. We find that φc = 0.676 339 ± 0.000 004, thus providing an extra significant digit of accuracy to this constant. (Some figures in this article appear in colour in the electronic version; see www.iop.org)

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