ORDERING AND DEMIXING TRANSITIONS IN MULTICOMPONENT WIDOM-ROWLINSON MODELS

We use Monte Carlo techniques and analytical methods to study the phas e diagram of multicomponent Widom-Rowlinson models on a square lattice : there are M species all with the same fugacity z and a nearest-neigh bor hard-core exclusion between unlike particles. Simulations show tha t for M between 2 and 6 there is a direct transition from the gas phas e at z < z(d)(M) to a demixed phase consisting mostly of one species a t z > z(d)(M), while for M greater than or equal to 7 there is an inte rmediate ''crystal phase'' for z lying between z(e)(M) and z(d)(M). In this phase, which is driven by entropy, particles, independent of spe cies, preferentially occupy one of the sublattices, i.e., spatial symm etry but not particle symmetry is broken. The transition at Z(d)(M) ap pears to be first order for M greater than or equal to 5, putting it i n the Potts model universality class. For large M the transition betwe en the crystalline and demixed phases at Id(M) can be proven to be fir st order with Z(d)(M)similar to M - 2 + 1/M+..., while z(e)(M) is argu ed to behave as lambda(cr)/M, with lambda(cr) the critical value of th e fugacity at which the one-component hard square lattice gas has a tr ansition, and to be always of the Ising type. Explicit calculations fo r the Bethe lattice with the coordination number q = 4 give results si milar 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, consisten t with the model being in the Potts universality class.