{"paper":{"title":"Critical behaviour of the XY -rotors model on regular and small world networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Sarah De Nigris (CPT), Xavier Leoncini (CPT)","submitted_at":"2013-04-17T15:13:03Z","abstract_excerpt":"We study the XY-rotors model on small networks whose number of links scales with the system size $N_{links}\\sim N^{\\gamma}$, where $1\\le\\gamma\\le2$. We first focus on regular one dimensional rings in the microcanonical ensemble. For $\\gamma<1.5$ the model behaves like short-range one and no phase transition occurs. For $\\gamma>1.5$, the system equilibrium properties are found to be identical to the mean field, which displays a second order phase transition at a critical energy density $\\varepsilon=E/N, \\varepsilon_{c}=0.75$. Moreover for $\\gamma_{c}\\simeq1.5$ we find that a non trivial state e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4854","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"}