{"paper":{"title":"A Cluster Expansion and the Decay of Correlations of the 1D Long-Range Ising Model at Low Temperatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Henrique Corsini, Rodrigo Bissacot","submitted_at":"2026-02-12T22:11:52Z","abstract_excerpt":"In this work, a convergent low-temperature cluster expansion of the one-dimensional long-range ferromagnetic Ising model with polynomial decay $\\alpha\\in (1,2]$ is developed; that is, $J(r)=r^{-\\alpha}$. As an application, the $n$-point correlations are studied and the two-point correlation is shown to be algebraic with rate of decay exactly $\\alpha$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.12447","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.12447/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}