{"paper":{"title":"Stationary point approach to the phase transition of the classical XY chain with power-law interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Michael Kastner","submitted_at":"2010-11-23T10:32:43Z","abstract_excerpt":"The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\\alpha}} with the distance) are analyzed. For a class of \"spinwave-type\" stationary points, the asymptotic behavior of the Hessian determinant of H is computed analytically in the limit of large system size. The computation is based on the Toeplitz property of the Hessian and makes use of a Szeg\\\"o-type theorem. The results serve to illustrate a recently discovered relation between phase transitions and the properties of stationary points of classical many-body Hamilt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5050","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"}