Jamming and percolation of dimers in restricted-valence random sequential adsorption

TL;DR

This paper investigates how restricted-valence random sequential adsorption affects percolation and jamming on square and triangular lattices, revealing a continuous transition and universality class consistent with standard percolation.

Contribution

It provides the first analysis of percolation thresholds and universality classes in restricted-valence RSA on different lattices, including disordered cases.

Findings

Percolation does not occur for maximum valence V_max=2 on the square lattice.

Percolation threshold increases with average valency.

Transitions belong to the standard percolation universality class.

Abstract

Restricted-valence random sequential adsorption~(RSA) is studied in its pure and disordered versions, on the square and triangular lattices. For the simplest case~(pure on the square lattice) we prove the absence of percolation for maximum valence $V_{\rm max}=2$. In other cases, Monte Carlo simulations are used to investigate the percolation threshold, universality class, and jamming limit. Our results reveal a continuous transition for the majority of the cases studied. The percolation threshold is computed through finite-size scaling analysis of seven properties; its value increases with the average valency. Scaling plots and data-collapse analyses show that the transition belongs to the standard percolation universality class even in disordered cases