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

TL;DR

This paper studies percolation phenomena in a two-species antagonistic RSA model on a 2D lattice, identifying a critical point where species A and blocked sites percolate, and provides exact low-density behavior formulas.

Contribution

It introduces a detailed analysis of percolation transitions in a two-species RSA model, including exact low-density coverage formulas and methods to accurately locate the transition point.

Findings

Percolation transition occurs at a critical probability x_A ≈ 0.6264.

Percolation behavior aligns with ordinary percolation universality.

Exact low-density coverage formulas for species A and B on z-coordinated lattices.

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.