Site percolation for a class of constrained honeycomb lattices

We consider site percolation in a class of correlated random media derived from randomly bi-colored triangular lattices. Media are constructed due to specific state-dependent local constraints. Constraints destroy stochastic independence of elementary events and have specific impact on site percolation thresholds. Further, a connection to critical concentrations of spontaneous magnetization in random 2D±J Ising models, at groundstates, is discussed.