Ordering and demixing transitions in multicomponent Widom-Rowlinson models

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest-neighbor hard-core exclusion between unlike particles. Simulations show that for M between 2 and 6 there is a direct transition from the gas phase at z < z(d)(M) to a demixed phase consisting mostly of one species at z > z(d)(M), while for M greater than or equal to 7 there is an intermediate ''crystal phase'' for z lying between z(e)(M) and z(d)(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e., spatial symmetry but not particle symmetry is broken. The transition at Z(d)(M) appears to be first order for M greater than or equal to 5, putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phases at Id(M) can be proven to be first order with Z(d)(M)similar to M - 2 + 1/M+..., while z(e)(M) is argued to behave as lambda(cr)/M, with lambda(cr) the critical value of the fugacity at which the one-component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q = 4 give results similar to those for the square lattice, except that the transition at z(d)(M) becomes first order at M > 2. This happens for all q, consistent with the model being in the Potts universality class.