Percolation with a periodic boundary condition: The effect of system size for crystallization in molecular dynamics

The effect of a periodic boundary condition (PBC) is examined for the percolation process in a square and in simple cubic lattices by means of a Monte Carlo simulation. The universality of the critical exponent for correlation length is valid even for the systems with PBC. The threshold pc for PBC coincides with the threshold for a free boundary condition in the site percolation of these lattices. We examine the effect of PBC for crystallization processes observed in the molecular dynamics simulation.