Percolation and jamming of random sequential adsorption samples of large linear k -mers on a square lattice

The behavior of the percolation threshold and the jamming coverage for isotropic random sequential adsorption samples has been studied by means of numerical simulations. A parallel algorithm that is very efficient in terms of its speed and memory usage has been developed and applied to the model involving large linear k -mers on a square lattice with periodic boundary conditions. We have obtained the percolation thresholds and jamming concentrations for lengths of k -mers up to 2¹⁷. A large k regime of the percolation threshold behavior has been identified. The structure of the percolating and jamming states has been investigated. The theorem of Kondrat, Koza, and Brzeski [Phys. Rev. E 96, 022154 (2017), 10.1103/PhysRevE.96.022154] has been generalized to the case of periodic boundary conditions. We have proved that any cluster at jamming is a percolating cluster and that percolation occurs before jamming.