Fast Monte Carlo algorithm for site or bond percolation

M. E. J. Newman, R. M. Ziff
2001 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
We describe in detail a new and highly efficient algorithm for studying site or bond percolation on any lattice. The algorithm can measure an observable quantity in a percolation system for all values of the site or bond occupation probability from zero to one in an amount of time which scales linearly with the size of the system. We demonstrate our algorithm by using it to investigate a number of issues in percolation theory, including the position of the percolation transition for site
more » ... ion for site percolation on the square lattice, the stretched exponential behavior of spanning probabilities away from the critical point, and the size of the giant component for site percolation on random graphs.
doi:10.1103/physreve.64.016706 pmid:11461441 fatcat:76uvr3npbff6nnvyiqr5dkoft4