Phase transitions for the Widom--Rowlinson model in random environments

TL;DR

This paper investigates phase transitions in the Widom--Rowlinson model within random environments, establishing conditions for non-uniqueness and phase transitions using inhomogeneous Poisson and Cox point processes.

Contribution

It introduces new non-uniqueness regimes and phase transition results for the Widom--Rowlinson model in complex random environments with percolation.

Findings

Non-uniqueness regimes established for the model.

Almost-sure phase transition results obtained.

Application to translation-invariant and ergodic Cox processes.

Abstract

We establish non-uniqueness regimes for the infinite-volume two-colored Widom--Rowlinson model based on inhomogeneous Poisson point processes with locally finite intensity measures featuring percolation. As an application, we provide almost-sure phase-transition results for the Widom--Rowlinson model based on translation-invariant and ergodic Cox point processes with stabilizing and non-stabilizing directing measures.