Analytical approximation of the inverse percolation thresholds for dimers on square, triangular and honeycomb lattices

Abstract

In this paper, an analytical approach to calculate inverse percolation thresholds in two-dimensional lattices is proposed. The new theoretical framework is obtained as a generalization of the analytical approximation introduced by Rosowsky (2000 Eur. Phys. J. B 15 77), in which the percolating particles are removed from an initially fully occupied cell. In addition, the traditional assumption that the calculation cell composed by one central site and its first and second nearest neighbors is replaced by the assumption that the cell is composed by two central sites and the corresponding first and second nearest neighbors. The resulting methodology was applied to calculate the inverse percolation thresholds corresponding to three systems: dimers removed from square lattices (pc = 0.5810), dimers removed from honeycomb lattices (pc = 0.7019) and dimers removed from triangular lattices (pc = 0.5125). The obtained results are discussed and compared with previous values calculated by very accurate simulations.