{"paper":{"title":"A continuous family of equilibria in ferromagnetic media are ground states","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.AP","math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Rafael de la Llave, Xifeng SU","submitted_at":"2015-06-11T08:15:39Z","abstract_excerpt":"We show that a foliation of equilibria (a continuous family of equilibria whose graph covers all the configuration space) in ferromagnetic models are ground states.\n  The result we prove is very general, and it applies to models with long range interactions and many body. As an application, we consider several models of networks of interacting particles including models of Frenkel-Kontorova type on $\\mathbb{Z}^d$ and one-dimensional quasi-periodic media.\n  The result above is an analogue of several results in the calculus variations (fields of extremals) and in PDE's. Since the models we consi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03582","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"}