Abstract
Continuous percolation of finite lines randomly distributed in two dimensions is studied numerically. Two finite-size effects in the distributions of critical percolation densities as a function of the system size are clearly distinguished for the first time in this system. The first one is a rounding of the distribution due to the finite size of the system. The second effect is a shift of the percolation threshold average. The rounding is well described by standard finite-size scaling whereas the shift is not and stems from a perimeter over surface correction. The numerical values of the critical exponents governing the rounding and the probability P ∞ for a line to belong to the percolating cluster are found to be in good agreement with theoretical predictions.
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