Journal of Statistical Physics, 1Iol. 21, No. 5, 1979 Percolation and Cluster Distribution. III. Algorithms for the Site-Bond Problem J. Hoshen, ~ P. Klymko, 1 and R. Kopelman 1 Received March 26, 1979," revised May 26, 1979 Algorithms for estimating the percolation probabilities and cluster size distribution are given in the framework of a Monte Carlo simulation for disordered lattices for the generalized site-bond problem. The site-bond approach is useful when a percolation process cannot be exclusively de- scribed in the context of pure site or pure bond percolation. An extended multiple labeling technique (ECMLT) is introduced for the generalized problem. The ECMLT is applied to the site-bond percolation problem for square and triangular lattices. Numerical data are given for lattices containing up to 16 million sites. An application to polymer gelation is suggested. KEY WORDS: Percolation zone; Monte Carlo; site-bond; tree; UNION operation; FIND operation. 1. INTRODUCTION The concept of percolation has been useful in describing a variety of physical, chemical, and biological phenomenaJ 1-3~ Two distinct types of percolation processes are recognized. These are bond percolation and site percolation. Permeation of fluids through porous media (4~ and gel formation by polymers via cross-linking (5/can be explained in terms of the bond percolation theory, ~ whereas crystal phenomena, such as spontaneous magnetization of dilute ferromagnets, ~6) diffusion in binary alloys, (7,8) and exciton percolation in molecular crystals, (9,1~ are described within the framework of site percolation. Site and bond percolation processes have both been suggested for electrical conductivity models of disordered materials. (11-~ The calculation of real lattice percolation parameters, such as percolation threshold, percolation probabilities, and cluster size distribution, proved not Supported by NSF Grant DMR76-07832 and NIH Grant NS08116-9. 1 Department of Chemistry, University of Michigan, Ann Arbor, Michigan. fi83 0022-4715/79/1100-0583$03.00]0 9 1979 PlenumPublishing Corporation