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Jamming and percolation of square objects of size $k \times k$ ($k^2$-mers)isotropically deposited on simple cubic lattices have been studied by numericalsimulations complemented with finite-size scaling theory. The $k^2$-mers wereirreversibly deposited into the lattice. Jamming coverage $\theta_{j,k}$ wasdetermined for a wide range of $k$ ($2 \leq k \leq 200$). $\theta_{j,k}$exhibits a decreasing behavior with increasing $k$, being$\theta_{j,k\rightarrow\infty}=0.4285(6)$ the limit value for large $k^2$-mersizes. On the other hand, the obtained results shows that percolationthreshold, $\theta_{c,k}$, has a strong dependence on $k$. It is a decreasingfunction in the range $2 \leq k \leq 18$ with a minimum around $k=18$ and, for$k \geq 18$, it increases smoothly towards a saturation value. Finally, acomplete analysis of critical exponents and universality has been done, showingthat the percolation phase transition involved in the system has the sameuniversality class as the 3D random percolation, regardless of the size $k$considered.

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