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


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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