THE ANALYSIS OF THE WIDOM-ROWLINSON MODEL BY STOCHASTIC GEOMETRIC METHODS

We study the continuum Widom-Rowlinson model of interpenetrating spheres. Using a new geometric representation for this system, we provide a simple percolation-based proof of the phase transition. We also use this representation to formulate the problem, and prove the existence of an interfacial tension between coexisting phases. Finally, we ascribe geometric (i.e. probabilistic) significance to the correlation functions which allows us to prove the existence of a sharp correlation length in the single-phase regime.