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