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

RAMIREZ L. S.; CENTRES, PAULO; RAMIREZ-PASTOR, ANTONIO JOSE; LEBRECHT, W.

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

IOP PUBLISHING LTD

Lugar: Londres; Año: 2019

1742-5468

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