Percolation in two-species antagonistic random sequential adsorption in two dimensions

Abstract

We consider two-species random sequential adsorption (RSA) in which species A and B adsorb randomly on a lattice with the restriction that opposite species cannot occupy nearest-neighbor sites. When the probability $x_A$ of choosing an A particle for an adsorption trial reaches a critical value $0.626441(1)$, the A species percolates and/or the blocked sites X (those with at least one A and one B nearest neighbor) percolate. Analysis of the size-distribution exponent $\tau$, the wrapping probabilities, and the excess cluster number shows that the percolation transition is consistent with that of ordinary percolation. We obtain an exact result for the low $x_B=1-x_A$ jamming behavior: ${\theta }_A=1-x_B+b_2{x}_B^2+\mathcal{O}(x_B^3)$, ${\theta }_B=x_B/(z+1)+\mathcal{O}(x_B^2)$ for a $z$-coordinated lattice, where ${\theta }_A$ and ${\theta }_B$ are respectively the saturation coverages of species A and B. We also show how differences between wrapping probabilities of A and X clusters, as well as differences in the number of A and X clusters, can be used to find the transition point accurately. For the one-dimensional case a three-site approximation appears to provide exact results for the coverages.

References in corpus (4)

• Percolation in Finite Matching Lattices
• Jamming and percolation of dimers in restricted-valence random sequential adsorption
• Interplay between thermal percolation and jamming upon dimer adsorption on binary alloys
• Jamming and percolation in the random sequential adsorption of a binary mixture on the square lattice

Cited by in corpus (2)

• Two-stage random sequential adsorption of discorectangles and disks on a two-dimensional surface
• One-dimensional $AB$ random sequential adsorption with one deposition per site