Cluster decomposition of percolation probability on the hexagonal lattice
E. S. Antonova, Yu. P. Virchenko
TL;DR
This paper provides an upper bound estimate for the percolation threshold on the hexagonal lattice using a cluster decomposition approach, analyzing cycle structures to understand cluster boundaries.
Contribution
It introduces a novel method for estimating the percolation threshold based on cycle enumeration and cluster decomposition on the hexagonal lattice.
Findings
Upper estimate of the percolation threshold is established.
Cycle enumeration bounds the size of finite clusters.
Method enhances understanding of cluster boundaries in percolation models.
Abstract
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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Taxonomy
TopicsStochastic processes and statistical mechanics · Random Matrices and Applications · Bayesian Methods and Mixture Models