Density profile of the incipient infinite percolation cluster

摘要

Monte Carlo simulations show simple scaling for the number of sites in the spanning cluster at the percolation threshold as a function of distance from the border. The results for free boundary conditions represent crossover from surface to bulk fractal dimensions, and the former agrees with exact results in d = 2 and d = 6－#epsilon# dimensions and with earlier simulations. We aslo present and explain results for bus-bar boundary conditions, with two types of connection rules. The scaling functions, which are predicted to be universal, surprisingly seem not to depend in the aspect ratios of the samples.