In conventional site percolation, all lattice sites are occupied with the same probability. For a bipartite lattice, sublattice-selective percolation instead involves two independent occupation probabilities, depending on the sublattice to which a given site belongs. Here, we determine the corresponding phase diagram for the two-dimensional square and Lieb lattices from quantifying the parameter regime where a percolating cluster persists for sublattice-selective percolation. For this purpose, we present an adapted Newman-Ziff algorithm. We also consider the critical exponents at the percolation transition, confirming previous Monte Carlo and renormalization-group findings that suggest sublattice-selective percolation belongs to the same universality class as conventional site percolation. To further strengthen this conclusion, we finally treat sublattice-selective percolation on the Bethe lattice (infinite Cayley tree) by an exact solution.

• Received 3 February 2024
• Accepted 11 March 2024

DOI:https://doi.org/10.1103/PhysRevE.109.044108