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 phas e diagram of the M-component Widom-Rowlinson model on the bce lattice: there are M species all with the same fugacity = and a nearest-neighb or hard core exclusion between unlike particles. Simulations show that for M greater than or equal to 3 there is a ''crystal phase'' for = l ying between z(c)(M) and z(d)(M) while for z > z(d)(M) there are M dem ixed phases each consisting mostly of one species. For M = 2 there is a direct second-order transition from the gas phase to the demixed pha se while for M greater than or equal to 3 the transition at z(d)(M) ap pears to be first order putting it in the Potts model universality cla ss. For M large, Pirogov-Sinai theory gives z(d)(M) similar to M - 2 2/(3M(2)) +.... In the crystal phase the particles preferentially occ upy one of the sublattices, independent of species, i.e. spatial symme try but not particle symmetry is broken, For M --> infinity this trans ition approaches that of the one-component hard cube gas with fugacity y = zM. We find by direct simulations of such a system a transition a t y(c) similar or equal to 0.71 which is consistent with the simulatio n z(c)(M) for large M. This transition appears to be always of the Isi ng type.