{"paper":{"title":"Gibbsianness and non-Gibbsianness in divide and color models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Andr\\'as B\\'alint","submitted_at":"2008-12-12T15:34:11Z","abstract_excerpt":"For parameters $p\\in[0,1]$ and $q>0$ such that the Fortuin--Kasteleyn (FK) random-cluster measure $\\Phi_{p,q}^{\\mathbb{Z}^d}$ for $\\mathbb{Z}^d$ with parameters $p$ and $q$ is unique, the $q$-divide and color [$\\operatorname {DaC}(q)$] model on $\\mathbb{Z}^d$ is defined as follows. First, we draw a bond configuration with distribution $\\Phi_{p,q}^{\\mathbb{Z}^d}$. Then, to each (FK) cluster (i.e., to every vertex in the FK cluster), independently for different FK clusters, we assign a spin value from the set $\\{1,2,\\...,s\\}$ in such a way that spin $i$ has probability $a_i$. In this paper, we p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2399","kind":"arxiv","version":4},"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"}