M. E. J. Newman, R. M. Ziff
Published 2001-01-18, updated 2001-04-08Version 2
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 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.
Comments: 17 pages, 13 figures. Corrections and some additional material in this version. Accompanying material can be found on the web at http://www.santafe.edu/~mark/percolation/
Journal: Phys. Rev. E 64, 016706 (2001)
Site Percolation on Planar $Φ^{3}$ Random Graphs
Redefinition of site percolation in light of entropy and the second law of thermodynamics
Robustness of Random Graphs Based on Natural Connectivity
