Jamming and percolation of k^{3}-mers on simple cubic lattices

Jamming and percolation of three-dimensional (3D) k×k×k cubic objects (k^{3}-mers) deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The k^{3}-mers were irreversibly deposited into the lattice. Jamming coverage θ_{j,k} was determined for a wide range of k (2≤k≤40). θ_{j,k} exhibits a decreasing behavior with increasing k, being θ_{j,k=∞}=0.4204(9) the limit value for large k^{3}-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, and the corresponding spatial correlation length critical exponent ν_{j} was measured, being ν_{j}≈3/2. However, the obtained results for the percolation threshold θ_{p,k} showed that θ_{p,k} is an increasing function of k in the range 2≤k≤16. For k≥17, all jammed configurations are nonpercolating states, and consequently, the percolation phase transition disappears. The interplay between the percolation and the jamming effects is responsible for the existence of a maximum value of k (in this case, k=16) from which the percolation phase transition no longer occurs. 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.