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

  title={Analytical approximation of the site percolation thresholds for monomers and dimers on two-dimensional lattices},
  author={Wolfram Lebrecht and Paulo M. Centres and Antonio Jos{\'e} Ramirez-Pastor},
  journal={Physica A: Statistical Mechanics and its Applications},
6 Citations

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

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

New bounds for the site percolation threshold of the hexagonal lattice

  • J. Wierman
  • Computer Science
    Journal of Physics A: Mathematical and Theoretical
  • 2022
The site percolation threshold of the hexagonal lattice satisfies 0.656 246 < p c < 0.739 695, and this bound is obtained by using the substitution method to compare the hexagon lattice site model to an exactly-solved two-parameter site perColation model on the martini lattice.

Percolation and jamming properties in particle shape-controlled seeded growth model

We consider the percolation model with nucleation and simultaneous growth of multiple finite clusters, taking the initial seed concentration ρ\documentclass[12pt]{minimal} \usepackage{amsmath}



Percolation transitions in two dimensions.

The amplitude of the power-law correction associated with X_{t2}=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems.

Dimer site-bond percolation on a triangular lattice

A generalization of the site-percolation problem, in which pairs of neighbor sites (site dimers) and bonds are independently and randomly occupied on a triangular lattice, has been studied by means

An analytical method to compute an approximate value of the site percolation threshold Pc

An analytical method to compute the site percolation threshold is introduced and yields an approximate value of Pc larger or equal to the real value.

Dimer site-bond percolation on a square lattice

Abstract.A generalization of the pure site and pure bond percolation problems in which pairs of nearest neighbor sites (site dimers) and linear pairs of nearest neighbor bonds (bond dimers) are

High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal

Percolation of aligned dimers on a square lattice

AbstractPercolation and jamming phenomena were investigated for anisotropic sequential deposition of dimers (particles occupying two adjacent adsorption sites) on a square lattice. The influence of