Jamming and percolation of k 2-mers on simple cubic lattices

Abstract

Jamming and percolation of square objects of size k × k (k2-mers) isotropically deposited on simple cubic lattices have been studied bynumerical simulations complemented with finite-size scaling theory. The k2-mers were irreversibly deposited into the lattice. Jamming coverage j,k wasdetermined for a wide range of k (2 k 200). j,k exhibits a decreasingbehavior with increasing k, being j,k = 0.4285(6) the limit value for largek2-mer sizes. On the other hand, the obtained results shows that percolationthreshold, c,k, has a strong dependence on k. It is a decreasing function in therange 2 k 18 with a minimum around k = 18 and, for k 18, it increasessmoothly towards a saturation value. Finally, a complete analysis of criticalexponents and universality has been done, showing that the percolation phasetransition involved in the system has the same universality class as the 3Drandom percolation, regardless of the size k considered.