NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2001, Volume 4, Number 2, pp.150-156


Coexistence of the Spanning Clusters with Percolation on a Square Lattice above Percolation Threshold
P.S.Grinchuk, N.V.Pavlyukevich, S.Borodetsky, and S.Rozin

One from actual problems of the percolation theory which has many applications is considered. The Monte-Carlo method is used to investigate the possibility of simultaneous existence of two clusters above the percolation threshold, when the clusters connect the opposite sides of a percolation system. Consideration is given to the site problem on a two-dimensional square lattice. An algorithm is suggested for such an investigation. It is found that the probability of coexistence of these clusters is a nonmonotonic function of the relative density of occupied sites that has a maximum at the point differing from the percolation threshold. It is shown that the position of this maximum depends on the lattice size. As the lattice size increases, the point of the maximum of probability tends to the percolation threshold. A qualitative explanation is given concerning the specific features of the behavior of the investigated probability, which have been revealed in computer simulation.
Key words: percolation theory, Monte-Carlo method, site problem, spanning cluster

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