Polychromatic percolation: Coexistence of percolating species in highly connected lattices

A generalization of percolation from a two-species (black-and-white) random process to a multispecies (polychromatic) process has been developed. The division of the chromatic composition field into regions in which different numbers of colors percolate for C colors on a lattice with percolation threshold pc has been analyzed. A panchromatic regime (all species percolate) occurs when C<pc^-1, occupying a fraction (1-Cpc)^C-1 of the composition field. Since polychromatic percolation has greatest scope for highly connected low-pc lattices, these ideas have been applied to site-percolation processes on d-dimensional close-packed lattices, as well as $d=2$ and $d=3$ lattices with long-range interactions. Also the concept of a lattice-independent dimensional-invariant critical volume fraction for site percolation has been extended to $d=4$ and $d=5$, but is shown to fail for $d>8$. Possible applications of polychromatic percolation are briefly discussed.