The percolation of fibres with random orientations: a Monte Carlo study

Abstract

Monte Carlo numerical simulations of the percolation of sticks with random orientations on a cubic lattice are reported. Finite size scaling and the position space renormalisation group are used. As the length of the sticks is increased it is found that the critical probability decreases whereas the correlation length exponent remains, within experimental errors, the same as in classical 3D percolation. Comparison with previous experimental and numerical results on related systems leads to the emphasis of the importance of the excluded-volume condition.