Continuum Percolation of Rods

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Abstract
We determine the aspect-ratio dependence of the critical percolation threshold for various systems of rods. An exact expansion, due to Coniglio et al., tests the conjecture that the threshold is proportional to the inverse of the expected excluded volume. We confirm the conjecture, and show that the proportionality becomes equality, for isotropic rods in three dimensions, in the slender-rod limit. In this limit, the critical region in which nonclassical exponents are valid vanishes.