P. Nielaba and J. L. Lebowitz
Phase Transitions in the Multicomponent Widom--Rowlinson Model
and in Hard Cubes on the BCC--Lattice
(86K, LaTeX)
ABSTRACT. We use Monte Carlo techniques and analytical methods to study the phase
diagram of the $M$--component Widom--Rowlinson model on the bcc--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 $M
\geq 3$ there is a ``crystal phase'' for $z$ lying between $z_c(M)$ and
$z_d(M)$ while for $z > z_d(M)$ there are $M$ demixed phases each
consisting mostly of one species. For $M=2$ there is a direct second order
transition from the gas phase to the demixed phase while for $M \geq 3$ the
transition at $z_d(M)$ appears to be first order putting it in the Potts
model universality class. For $M$ large, Pirogov-Sinai theory gives
$z_d(M) \sim M-2+2/(3M^2) + ... $. In the crystal phase the particles
preferentially occupy one of the sublattices, independent of species, i.e.\
spatial symmetry but not particle symmetry is broken. For $M \to \infty$
this transition approaches that of the one component hard cube gas with
fugacity $y = zM$. We find by direct simulations of such a system a
transition at $y_c \simeq 0.71$ which is consistent with the simulation
$z_c(M)$ for large $M$. This transition appears to be always of the Ising
type.