LAUSR

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.