Breaking universality in random sequential adsorption on a square lattice with long-range correlated defects

Abstract

Jamming and percolation transitions in the standard random sequential adsorption of particles on regular lattices are characterized by a universal set of critical exponents. The universality class is preserved even in the presence of randomly distributed defective sites that are forbidden for particle deposition. However, using large-scale Monte Carlo simulations by depositing dimers on the square lattice and employing finite-size scaling, we provide evidence that the system does not exhibit such well-known universal features when the defects have spatial long-range (power-law) correlations. The critical exponents $\nu_j$ and $\nu$ associated with the jamming and percolation transitions, respectively, are found to be non-universal for strong spatial correlations and approach systematically their own universal values as the correlation strength is decreased. More crucially, we have found a difference in the values of the percolation correlation length exponent $\nu$ for a small but finite density of defects with strong spatial correlations. Furthermore, for a fixed defect density, it is found that the percolation threshold of the system, at which the largest cluster of absorbed dimers first establishes the global connectivity, gets reduced with increasing the strength of the spatial correlation.