Phase transitions of a multicomponent Widom-Rowlinson model

Abstract

We study a multicomponent version of the ``A−B'' model of Widom and Rowlinson, generalized in a symmetric way: There is an infinite repulsive interaction between any two unlike particles. We consider both lattice and continuum versions of the model and show that the ``demixing'' transition occurs for any finite number M of components, all having the same activity. No conclusion can be drawn about this transition in the limit M→∞. It is shown, however, that another transition, in which the density is greater on one of the sublattices, appears at a finite value of M which persists for all larger M at any fixed value of the activity. In the limit M→∞, z→0, M z=ζ, const, this system apparently becomes ``equivalent'' to a one‐component system with activity ζ in which there is an exclusion for occupancy of nearest neighbor sites. The latter transition then becomes the ``hard square'' transition.