Percolation Thresholds in the Three-Dimensional Sticks System

We report the dependence of the percolation threshold of the three-dimensional sticks systems on aspect ratio and on macroscopic anisotropy. This Monte Carlo study is the first determination of percolation thresholds for randomly oriented objects in three-space. The results show that the above dependence is determined by the excluded volume of the sticks. However, the total excluded volume of randomly oriented objects is lower than that of the same objects in parallel alignment.