{"paper":{"title":"A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Ron Peled, Yinon Spinka","submitted_at":"2017-12-11T09:53:40Z","abstract_excerpt":"We give a general condition for a discrete spin system with nearest-neighbor interactions on the $\\mathbb{Z}^d$ lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order is entropically driven. As a main example we consider the antiferromagnetic $q$-state Potts model and rigorously prove the existence of a broken sub-lattice symmetry phase at low temperature and high dimension -- a new result for $q\\ge 4$. As further examples, we prove the existence of an ordered phase in a clock model with hard constraints and extend the kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03699","kind":"arxiv","version":2},"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"}