{"paper":{"title":"Hard-Core and Soft-Core Widom-Rowlinson models on Cayley trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christof Kuelske, Sascha Kissel, Utkir A. Rozikov","submitted_at":"2019-01-26T18:19:33Z","abstract_excerpt":"We consider both Hard-Core and Soft-Core Widom-Rowlinson models with spin values $-1,0,1$ on a Cayley tree of order $k\\geq 2$ and we are interested in the Gibbs measures of the models. The models depend on 3 parameters: the order $k$ of the tree, $\\theta$ describing the strength of the (ferromagnetic or antiferromagnetic) interaction, and $\\lambda$ describing the intensity for particles. The Hard-Core Widom-Rowlinson model corresponds to the case $\\theta=0$. For the binary tree $k=2$, and for $k=3$ we prove that the ferromagnetic model has either one or three splitting Gibbs measures (tree-aut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.09258","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":""},"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"}