Monte Carlo studies of percolation phenomena for a simple cubic lattice

The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates for p_c (0.3115±0.0005), β (0.41±0.01), γ (1.6±0.1), and ν(0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average "surface area" for clusters of size k is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizes k is found to have an exponential tail for large values of k for P <p_c. For p >p_c there is too much scatter in the data to draw firm conclusions about the size distribution.