WIAS Preprint No. 3054, (2023)

Locality properties for discrete and continuum Widom--Rowlinson models in random environments


  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Külske, Christof
  • Zass, Alexander
    ORCID: 0000-0001-6124-842X

2020 Mathematics Subject Classification

  • 60K35 60G55 60G60 82B20 82B21


  • Gibbs measures, quasilocality, point processes, Widom--Rowlinson models, Papangelou intensities, disordered systems




We consider the Widom--Rowlinson model in which hard disks of two possible colors are constrained to a hard-core repulsion between particles of different colors, in quenched random environments. These random environments model spatially dependent preferences for the attach- ment of disks. We investigate the possibility to represent the joint process of environment and infinite-volume Widom--Rowlinson measure in terms of continuous (quasilocal) Papangelou inten- sities. We show that this is not always possible: In the case of the symmetric Widom-Rowlinson model on a non-percolating environment, we can explicitly construct a discontinuity coming from the environment. This is a new phenomenon for systems of continuous particles, but it can be understood as a continuous-space echo of a simpler non-locality phenomenon known to appear for the diluted Ising model (Griffiths singularity random field [ EMSS00]) on the lattice, as we explain in the course of the proof.

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