{"paper":{"title":"Lattice random-field Widom--Rowlinson models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benedikt Jahnel, Christof K\\\"ulske, Daniel Kamecke","submitted_at":"2026-05-18T17:58:51Z","abstract_excerpt":"We consider the Widom--Rowlinson model on $\\mathbb{Z}^d$ subject to a symmetric i.i.d.\\ random field. We prove that for dimensions $d\\le 2$ any non-trivial random field leads to an absence of a phase transition. In contrast, in dimensions $d\\ge 3$ and for Gaussian random fields, phase-transition behavior of the model is maintained for sufficiently large densities of occupied sites. This extends the general picture known from the classical random-field Ising model to the random-field Widom--Rowlinson model. Following the general proof route of Aizenman--Wehr as well as Ding--Zhuang, our main co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18744","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18744/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:58.993400Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6186ebf7da53bbb7bca5fa0db4d07837dc8d16a5949124c3f69652d3fe2b1f11"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}