Jamming of dimers on d-dimensional substrates

CENTRES, P.M.; RAMIREZ L. S.; CWILICH, G. A.; PASINETTI, P.M.; RAMIREZ PASTOR, A. J.

Congreso; 104a Reunion de la Asociacion Fisica Argentina; 2019

In the RSA scheme, dimers are randomly and sequentially deposited onto a discretesubstrate without overlapping each other. The quantity of interest is the fraction of latticesites covered at a time t by the deposited particles, θ(t). The process finishes when allunoccupied spaces are reduced to isolated sites where dimers can no longer be deposited,reaching a limiting or jamming state, being θ(t → ∞) < θj < 1. In general, θ ranges from 0to θj for objects occupying more than one site. The analytical determination of the jammingconcentration is a very difficult task, only possible for some particular cases, appealing ingeneral to numerical simulations to estimate the concentration and its dependence withthe parameters of the system. The determination of the jamming concentration can bedone 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 estimatednumerically. The study is carried out on d-dimensional substrates including 1D, 2D and3D regular lattices, as well as fractal substrates of intermediate dimensions, finding therelationship between the exponent ν and the dimension.