Some aspects of probability distribution for percolation of several fluids on the hexagonal lattice

We study random coloring of the hexagons of a honeycomb lattice into $2^{n-1}$ colors (that is the standard Potts model at infinite temperature). It may be considered as a generalization of percolation to $n$ pairwise independent, but mutually dependent liquids. We introduce a new observable that can be interpreted as the fraction of percolated liquids. An analogue of the central limit theorem for this observable is proved and several conjectures based on numeric experiments are proposed.