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

2025/05/08 by Benedikt Jahnel, Jahnel, Benedikt, Daniel Kamecke +1
Mathematics · #05C80 (Secondary) #60K35 (Primary) #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2505.05319

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Features of a spin glass in the random field Ising model
• Long range order for three-dimensional random field Ising model throughout the entire low temperature regime
• Continuum Percolation in a Nonstabilizing Environment
• Sharp phase transition for Cox percolation
• Phase transitions for the Boolean model of continuum percolation for Cox\n point processes
• Gibbs-non Gibbs transitions in different geometries: The Widom-Rowlinson\n model under stochastic spin-flip dynamics
• Sharp phase transition for the continuum Widom-Rowlinson model
• Continuum percolation for Cox point processes
• Introduction to the theory of Gibbs point processes
• Infinite Volume Continuum Random Cluster Model
• The random geometry of equilibrium phases

Related

• Sharp phase transition for the continuum Widom-Rowlinson model
• Locality properties for discrete and continuum Widom--Rowlinson models in random environments
• Gibbs-non Gibbs transitions in different geometries: The Widom-Rowlinson\n model under stochastic spin-flip dynamics
• Continuum percolation in a nonstabilizing environment
• Continuum Percolation in a Nonstabilizing Environment