Analytical approximation of the site percolation thresholds for monomers and dimers on two-dimensional lattices

摘要

In this paper, a theoretical approach to calculate site percolation thresholds on two-dimensional lattices is proposed. The method, based on exact counting of configurations on finite cells, arises as a generalization of the analytical approximation introduced by Rosowsky (2000). The resulting methodology was applied to calculate the percolation thresholds corresponding to four systems: monomers on honeycomb lattices (p(c) = 0.71278), dimers on square lattices (p(c) = 0.5713), dimers on honeycomb lattices (p(c) = 0.6653) and dimers on triangular lattices (p(c) = 0.4783). The obtained results are in good agreement with previous values calculated by very accurate simulations: 0.69704, 0.5649, 0.6902 and 0.4872. The technique can be easily extended to deal with three-dimensional lattices. (C) 2018 Elsevier B.V. All rights reserved.