{"paper":{"title":"Quantum Spin probabilities at positive temperature are H\\\"older Gibbs probabilities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP","quant-ph"],"primary_cat":"math.DS","authors_text":"Artur O. Lopes, Carlos G. Moreira, Jader E. Brasil, Jairo K. Mengue","submitted_at":"2018-05-04T13:49:20Z","abstract_excerpt":"We consider the KMS state associated to the Hamiltonian $H= \\sigma^x \\otimes \\sigma^x$ over the quantum spin lattice $\\mathbb{C}^2 \\otimes \\mathbb{C}^2 \\otimes \\mathbb{C}^2 \\otimes ...$.\n  For a fixed observable of the form $L \\otimes L \\otimes L \\otimes ...$, where $L:\\mathbb{C}^2 \\to \\mathbb{C}^2 $ is self adjoint, and for positive temperature $T$ one can get a naturally defined stationary probability $\\mu_T$ on the Bernoulli space $\\{1,2\\}^\\mathbb{N}$.\n  The Jacobian of $\\mu_T$ can be expressed via a certain continued fraction expansion.\n  We will show that this probability is a Gibbs proba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01784","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"}