On global site-percolation on the correlated honeycomb lattice

We consider global site percolation on a correlated bi-colored honeycomb lattice. The correlated medium is constructed from an independently randomly bi-colored triangular lattice due to a state dependent constraint. The constraint evokes short-range correlations and establishes a simple symmetry in the random system, thereby significantly affecting the systemʹs critical behavior. Particularly, there exist two phase transitions pc≈0.2902 and qc≈0.7097, these thresholds are shifted away from those expected in independent percolation. Values are in good agreement with bounds analytically derived here.