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

Abstract 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. Highlights • The percolation problem of monomers and dimers on 2D lattices is studied. • A theoretical approach based on counting configurations on finite cells is applied. • Percolation thresholds are reported. • The obtained results are in good agreement with previous calculations in the literature. [ABSTRACT FROM AUTHOR]