An Investigation of Site - Bond Percolation on Many Lattices

Site-bond percolation is a natural generalization of pure site percolation and pure bond percolation. The generalization allows both sites and bonds to be randomly occupied, with probabilities ps and pb respectively, in the case of random percolation. In particular, if pb = ps, site-bond percolation reduces to a pure site or pure bond percolation on a decorated lattice. It is also possible to introduce a correlation between the occupation probabilities of adjacent sites and bonds, which is usually referred to as correlated percolation. Site-bond percolation has many applications in different fields. For example, it was used to describe the sol-to-gel transition (gelation) of polymers, the spreading of an infection, etc. In site-bond percolation one looks for clusters of occupied sites, connected to each other by occupied bonds. When there is a cluster that connects one side of the system with the other, the system is said to percolate. First mentioned by Frisch and Hammersley, the model was investigated at first by Hoshen by means of Monte Carlo simulations. Agrawal et al. showed, using a series method, that the critical