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

W. Lebrecht, P.M. Centres and A.J. Ramirez-Pastor

Physica A: Statistical Mechanics and its Applications, 2019, vol. 516, issue C, 133-143

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 (pc=0.71278), dimers on square lattices (pc=0.5713), dimers on honeycomb lattices (pc=0.6653) and dimers on triangular lattices (pc=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.

Keywords: Statistical mechanics of model systems; Random sequential adsorption (RSA); Multisite-occupancy; Percolation; Computational methods in statistical physics and nonlinear dynamics (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:516:y:2019:i:c:p:133-143

DOI: 10.1016/j.physa.2018.10.023

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