The study of percolation with the presence of extended impurities

In the preceding paper, Budinski-Petković et al (2016 J. Stat. Mech. 053101) studied jamming and percolation aspects of random sequential adsorption of extended shapes onto a triangular lattice initially covered with point-like impurities at various concentrations. Here we extend this analysis to needle-like impurities of various lengths $\ell$. For a wide range of impurity concentrations p, percolation threshold ${\theta }_p^{\ast }$ is determined for k-mers, angled objects and triangles of two different sizes. For sufficiently large impurities, percolation threshold ${\theta }_p^{\ast }$ of all examined objects increases with concentration p, and this increase is more prominent for impurities of a larger length $\ell$. We determine the critical concentrations of defects $p_c^{\ast }$ above which it is not possible to achieve percolation for a given object, for impurities of various lengths $\ell$. It is found that the critical concentration $p_c^{\ast }$ of finite-size impurities decreases with the length $\ell$ of impurities. In the case of deposition of larger objects an exception occurs for point-like impurities when critical concentration $p_c^{\ast }$ of monomers is lower than $p_c^{\ast }$ for the dimer impurities. At relatively low concentrations p, the presence of small impurities (but not point-like) stimulates the percolation for larger depositing objects. (paper: classical statistical mechanics, equilibrium and non-equilibrium)