Jamming of dimers on d-dimensional substrates

Abstract

In the RSA scheme, dimers are randomly and sequentially deposited onto a discrete substrate without overlapping each other. The quantity of interest is the fraction of lattice sites covered at a time t by the deposited particles, θ (t). The process finishes when all unoccupied spaces are reduced to isolated sites where dimers can no longer be deposited, reaching a limiting or jamming state, being θ (t→∞) < θ J < 1. In general, θ ranges from 0 to θ J for objects occupying more than one site. The analytical determination of the jamming concentration is a very difficult task, only possible for some particular cases, appealing in general to numerical simulations to estimate the concentration and its dependence with the parameters of the system. The determination of the jamming concentration can be done through the probability WL( θ ) that a particular RSA process reaches the coverage θ . This quantity scales around the critical point with an exponent ν which can be estimated numerically. The study is carried out on d-dimensional substrates including 1D, 2D and 3D regular lattices, as well as fractal substrates of intermediate dimensions, finding the relationship between the exponent ν and the dimension.