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

Jamming and percolation of square objects of size ( k 2 -mers) isotropically deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The k 2 -mers were irreversibly deposited into the lattice. Jamming coverage was determined for a wide range of k ( ). exhibits a decreasing behavior with increasing k , being the limit value for large k 2 -mer sizes. On the other hand, the obtained results shows that percolation threshold, , has a strong dependence on k . It is a decreasing function in the range with a minimum around k = 18 and, for , it increases smoothly towards a saturation value. Finally, a complete analysis of critical exponents and universality has been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation, regardless of the size k considered.