Critical properties of random-site percolation in two and three dimensions: A Monte Carlo study

We measure the critical exponents of two-dimensional and three-dimensional random-site percolation and find excellent agreement with Nienhuis exact results (two-dimensions) and good agreement with other numerical work (three-dimensions). We also measure the correlation length amplitude ratio and the mean-cluster size amplitude ratio in two- and three- dimensions. We report values of 4.0 ± 0.5 (2d), 2.0 ± 0.5 (3d) and 75 (+40-26) (2d) and 8 (+3-2) (3d) for the correlation length and the mean cluster size amplitude ratios respectively. A direct measurement is made of the fractal dimension, df. At the critical point, pc(=0.50) of the triangular lattice df is 1.90 ± 0.01 while at pc = 0.3117 for the simple cubic lattice df is 2.50 ± 0.02.