97-450 J. L. Lebowitz, A. Mazel, P. Nielaba, and L. Samaj

Ordering and Demixing Transitions in Multicomponent Widom--Rowlinson Models (1877K, LaTeX) Aug 21, 97

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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.

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