{"paper":{"title":"A Mermin--Wagner theorem for Gibbs states on Lorentzian triangulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Yambartsev, M. Kelbert, Yu. Suhov","submitted_at":"2012-10-30T12:27:26Z","abstract_excerpt":"We establish a Mermin--Wagner type theorem for Gibbs states on infinite random Lorentzian triangulations (LT) arising in models of quantum gravity. Such a triangulation is naturally related to the distribution $\\sf P$ of a critical Galton--Watson tree, conditional upon non-extinction. At the vertices of the triangles we place classical spins taking values in a torus $M$ of dimension $d$, with a given group action of a torus ${\\tt G}$ of dimension $d'\\leq d$. In the main body of the paper we assume that the spins interact via a two-body nearest-neighbor potential $U(x,y)$ invariant under the ac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7981","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"}