Percolation on hypercubic lattices, which can be represented as $\mathbb{Z}^d$, where $d$ is the dimension of the lattice, and $\mathbb{Z}$ is the set of integers of course.

Some mathematical results exist for Percolation thresholds, and Continuity of percolation phase transition. In particular, it is known that the percolation threshold at dimension $d$ is greater than or equal that of dimension $d+1$ for percolation on $\mathbb{Z}^d$.