{"paper":{"title":"Ensemble Inequivalence in Long-Range Quantum Spin Systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Microcanonical and canonical ensembles produce different phase diagrams for long-range quantum ferromagnets at finite temperatures.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Daniel Arrufat-Vicente, David Mukamel, Nicolo Defenu, Stefano Ruffo","submitted_at":"2025-04-18T18:01:26Z","abstract_excerpt":"Ensemble inequivalence occurs when a systems thermodynamic properties vary depending on the statistical ensemble used to describe it. This phenomenon is known to happen in systems with long-range interactions and has been observed in many classical systems. In this study, we provide a detailed analysis of a long-range quantum ferromagnet spin model that exhibits ensemble inequivalence. At zero temperature ($T = 0$), the microcanonical phase diagram matches that of the canonical ensemble. However, the two ensembles yield different phase diagrams at finite temperatures. This behavior contrasts w"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"At finite temperatures the microcanonical and canonical ensembles yield different phase diagrams for the long-range quantum ferromagnet.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The specific long-range quantum ferromagnet spin model chosen for the analysis is representative of the general class of long-range quantum systems that exhibit ensemble inequivalence.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A long-range quantum ferromagnet exhibits ensemble inequivalence, with microcanonical and canonical phase diagrams agreeing at T=0 but diverging at finite temperatures.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Microcanonical and canonical ensembles produce different phase diagrams for long-range quantum ferromagnets at finite temperatures.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"fabbd8f1a3fe24126c313dca7fb6216931c7a8bcfe86ae05366f21ed1427b1b2"},"source":{"id":"2504.14008","kind":"arxiv","version":2},"verdict":{"id":"861aa94b-f8cb-4e66-864d-e64b47242e30","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T19:23:10.585063Z","strongest_claim":"At finite temperatures the microcanonical and canonical ensembles yield different phase diagrams for the long-range quantum ferromagnet.","one_line_summary":"A long-range quantum ferromagnet exhibits ensemble inequivalence, with microcanonical and canonical phase diagrams agreeing at T=0 but diverging at finite temperatures.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The specific long-range quantum ferromagnet spin model chosen for the analysis is representative of the general class of long-range quantum systems that exhibit ensemble inequivalence.","pith_extraction_headline":"Microcanonical and canonical ensembles produce different phase diagrams for long-range quantum ferromagnets at finite temperatures."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.14008/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":79,"sample":[{"doi":"","year":null,"title":"and f(mz = m∗ z) are both global minima of the free energy, i.e. f(mz = 0) = f(m∗ z) , ∂mz f(mz) mz=0 = ∂mz f(mz) mz=m∗z = 0 , (33) yielding the following conditions m∗ z = tanh β p h2 + (2J m∗z + 4Km","work_id":"36a46786-dac5-42f4-8467-d7f8987ee748","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":", J m∗ z 2 + 3Km ∗ z 4 + 1 β ln (coshβh) = 1 β ln cosh β q h2 + 2J m∗ + 4Km ∗3 2 , (34) whose solution is found numerically and reported in Fig. 1. 5 B. Microcanonical ensemble. To determine the secon","work_id":"6cc30799-27b2-4e34-903e-6ba8c0fc33fd","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"= 0 , h2m∗ z 2 + (ε + J m∗ z 2 + Km ∗ z 4)2 = ε2 . (46) The first equation expresses the requirement that the so- lution mz = ±m∗ z is a local extremum of the entropy, while the second equation result","work_id":"6bf0bed9-8afd-4529-9c2f-1ad69686a57d","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2003,"title":"Colloquium: Trapping and manipulating photon states in atomic ensembles,","work_id":"5b8b942f-7b9e-4f5d-98e9-278ca7e28b08","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"Quantum information with Rydberg atoms,","work_id":"ccf0382d-e3b8-4532-9b41-801241716b77","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":79,"snapshot_sha256":"f778c768dcb907e81288c23bbb19d2965621a415105e9f267e7cee5263266a9b","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"}