Reentrant disorder-disorder transitions in generalized multicomponent Widom-Rowlinson models

In the lattice version of the multicomponent Widom-Rowlinson (WR) model, each site can be either empty or singly occupied by one of $M$ different particles, all species having the same fugacity $z$. The only nonzero interaction potential is a nearest-neighbor hard-core exclusion between unlike particles. For $M<M_0$ with some minimum $M_0$ dependent on the lattice structure, as $z$ increases from 0 to $\infty$ there is a direct transition from the disordered (gas) phase to a demixed (liquid) phase with one majority component at $z>z_d(M)$. If $M\ge M_0$, there is an intermediate ordered "crystal phase" (composed of two nonequivalent even and odd sublattices) for $z$ lying between $z_c(M)$ and $z_d(M)$ which is driven by entropy. We generalize the multicomponent WR model by replacing the hard-core exclusion between unlike particles by more realistic large (but finite) repulsion. The model is solved exactly on the Bethe lattice with an arbitrary coordination number. The numerical calculations, based on the corner transfer matrix renormalization group, are performed for the two-dimensional square lattice. The results for $M=4$ indicate that the second-order phase transitions from the disordered gas to the demixed phase become of first order, for an arbitrarily large finite repulsion. The results for $M\ge M_0$ show that, as the repulsion weakens, the region of crystal phase diminishes itself. For weak enough repulsions, the direct transition between the crystal and demixed phases changes into a separate pair of crystal-gas and gas-demixed transitions; this is an example of a disorder-disorder reentrant transition via an ordered crystal phase. If the repulsion between unlike species is too weak, the crystal phase disappears from the phase diagram. It is shown that the generalized WR model belongs to the Ising universality class.