Three-dimensional percolation with removed lines of sites

The site percolation problem on a cubic lattice in which entire lines of sites are removed randomly is analyzed with use of both analytical and large-cell (up to 1003) Monte Carlo renormalization-group techniques. Because of strong correlation effects, the behavior of small systems deviates appreciably from regular percolation, and the percolation threshold is lowered. However, it is shown that the asymptotic values of the critical exponents are consistent with those of regular percolation. The results suggest a practical way to generate macroscopic three-dimensional percolating samples, which can be used to measure various physical properties of percolating systems.