Phase transitions in the multicomponent Widom-Rowlinson model and in hard cubes on the bcc lattice

We use Monte Carlo techniques and analytical methods to study the phase diagram of the M-component Widom-Rowlinson model on the bcc lattice: there are M species all with same fugacity z and a nearest-neighbor hard core exclusion between unlike particles. Simulations show that for M ⩾ 3 there is a “crystal phase” for z lying between zc(M) and zd(M) while for z > zd(M) there are M demixed phases each consisting mostly of one species. For M = 2 there is a direct second-order transition from the gas phase to the demixed phase while for M ⩾ 3 the transition at zd(M) appears to be first order putting it in the Potts model universality class. For M large, Pirogov-Sinai theory gives zd(M) ∼ M − 2 + 2/(3M2) + …. In the crystal phase the particles preferentially occupy one of the sublattices, independent of species, i.e. spatial symmetry but not particle symmetry is broken. For M → ∞ this transition approaches that of the one-component hard cube gas with fugacity y = zM. We find by direct simulations of such a system a transition at yc ≅ 0.71 which is consistent with the simulation zc(M) for large M. This transition appears to be always of the Ising type.