Condensed Matter Physics, 2014, vol. 17, No. 3, p. 33006:111
DOI:10.5488/CMP.17.33006
Title:
Jamming and percolation of parallel squares in singlecluster growth model
Author(s):

I.A. Kriuchevskyi
(Taras Shevchenko Kiev National University, Department of Physics, 2 Academician Glushkov Avenue, 031127 Kyiv, Ukraine)
,


L.A. Bulavin
(Taras Shevchenko Kiev National University, Department of Physics, 2 Academician Glushkov Avenue, 031127 Kyiv, Ukraine)
,


Yu.Yu. Tarasevich
(Astrakhan State University, 20a Tatishchev St., 414056 Astrakhan, Russia)
,


N.I. Lebovka
(Institute of Biocolloidal Chemistry named after F.D. Ovcharenko of the National Academy of Sciences of Ukraine, 42 Academician Vernadsky Boulevard, 03142 Kiev, Ukraine)

This work studies the jamming and percolation of parallel squares in a singlecluster growth model. The LeathAlexandrowicz 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 (Eproblem) or a mixture of k x k and m x m (m ≤ k) squares (Mproblem). The larger k x k squares were assumed to be active (conductive) and the smaller m x m squares were assumed to be blocked (nonconductive). For equal size k x k squares (Eproblem) the value of p_{j} = 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, p_{j} = 0.564 ± 0.002. It was observed that the value of percolation threshold p_{c} (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 (Mproblem), the value of p_{c} 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 Mproblem can be effectively suppressed in the presence of smaller blocked squares.
Key words:
jamming, percolation, squares, disordered systems, Monte Carlo methods, LeathAlexandrowicz method
PACS:
02.70.Uu, 05.65.+b, 36.40.Mr, 61.46.Bc, 64.60.ah
