## DIMACS TR: 97-09

## Phase Transitions in the Multicomponent Widom--Rowlinson Model
and in Hard Cubes on the BCC--Lattice

### Authors: P. Nielaba and J.L. Lebowitz

**
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.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-09.ps.gz

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