Cluster decomposition of percolation probability on the hexagonal lattice

Details Cluster decomposition of percolation probability on the hexagonal lattice Cluster decomposition of percolation probability on the hexagonal lattice

2009-09-07

arxiv.org/abs/0909.1312v2

Physics

Mathematical Physics

23 pages; 7 figures

Scientific paper

The upper estimate of the percolation threshold of the Bernoulli random field
on the hexagonal lattice is found. It is done on the basis of the cluster
decomposition. Each term of the decomposition is estimated using the number
estimate of cycles on the hexagonal lattice which represent external borders of
possible finite clusters containing the fixed lattice vertex.

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