J. L. Lebowitz, A. Mazel, P. Nielaba, and L. Samaj
Ordering and Demixing Transitions in Multicomponent Widom--Rowlinson Models
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ABSTRACT. 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 two and six 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 $M \geq 7$ there is an intermediate ``crystal
phase'' for $z$ lying between $z_c(M)$ 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 $M \geq 5$ putting it in the Potts model universality class. For
large $M$ the transition between the crystalline and demixed phase at
$z_d(M)$ can be proven to be first order with $z_d(M) \sim M-2 + 1/M +
...$, while $z_c(M)$ is argued to behave as $\mu_{cr}/M$, with $\mu_{cr}$
the 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.