{"paper":{"title":"Gibbs measures of disordered lattice systems with unbounded spins","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Tanja Pasurek, Yuri Kondratiev, Yuri Kozitsky","submitted_at":"2010-08-16T15:16:24Z","abstract_excerpt":"The Gibbs measures of a spin system on $Z^d$ with unbounded pair interactions $J_{xy} \\sigma (x) \\sigma (y)$ are studied. Here $\\langle x, y \\rangle \\in E $, i.e. $x$ and $y$ are neighbors in $Z^d$. The intensities $J_{xy}$ and the spins $\\sigma (x) , \\sigma (y)$ are arbitrary real. To control their growth we introduce appropriate sets $J_q\\subset R^E$ and $S_p\\subset R^{Z^d}$ and prove that for every $J = (J_{xy}) \\in J_q$: (a) the set of Gibbs measures $G_p(J)= \\{\\mu: solves DLR, \\mu(S_p)=1\\}$ is non-void and weakly compact; (b) each $\\mu\\inG_p(J)$ obeys an integrability estimate, the same f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2686","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"}