Efficient measurement of the percolation threshold for fully penetrable discs

Abstract

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 _c = 0.676 339±0.000 004, thus providing an extra significant digit of accuracy to this constant.