Refined Monte Carlo simulations of static percolation

Abstract

A modified Monte Carlo approach is used to derive and check the consistency of the critical site percolation concentrations and some critical exponents of the square and triangular lattices (with lo9 sites). While we confirm both universality and the accepted value for y and v (and c, for the triangular lattice), our c, value for the square lattice (c, = 0.5929 & 0.0002) is slightly higher than some recently quoted values. This reopens the, questions of methodology and lattice size. We also give effective y exponents for multiple layers, showing a monotonic crossover from two-dimensional to three-dimensional values. The preexponent is roughly unity over a wide concentration range.