, Volume 172, Issue 3, pp 551-569

The analysis of the Widom-Rowlinson model by stochastic geometric methods

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Abstract

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.

Partly supported by the grants GAČR 202/93/0499, GAUK 376, NSF-DMS 91-04487, and NSF-DMS 93-02023
Communicated by D. Brydges