Jamming and percolation of parallel squares in single-cluster growth model - Kriuchevskyi, I.A.; Bulavin, L.A.; Tarasevich, Yu.Yu.; Lebovka, N.I. (Condensed Matter Physics, 2014)
This work studies the jamming and percolation of parallel squares in a single-cluster growth model. The Leath-Alexandrowicz method was used to grow a cluster from an active seed site. The sites of a square lattice were occupied by addition of the equal size k x k squares (E-problem) or a mixture of k x k and m x m (m ≤ k) squares (M-problem). The larger k x k squares were assumed to be active (conductive) and the smaller m x m squares were assumed to be blocked (non-conductive). For equal size k x k squares (E-problem) the value of pj = 0.638 ± 0.001 was obtained for the jamming concentration in the limit of k →∞. This value was noticeably larger than that previously reported for a random sequential adsorption model, pj = 0.564 ± 0.002. It was observed that the value of percolation threshold pc (i.e., the ratio of the area of active k x k squares and the total area of k x k squares in the percolation point) increased with an increase of k. For mixture of k x k and m x m squares (M-problem), the value of pc noticeably increased with an increase of k at a fixed value of m and approached 1 at k ≥ 10 m. This reflects that percolation of larger active squares in M-problem can be effectively suppressed in the presence of smaller blocked squares.