{"paper":{"title":"Response to arXiv:1209.0731 'Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices' by Perk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.stat-mech","authors_text":"Norman H. March, Zhidong Zhang","submitted_at":"2012-09-12T07:23:24Z","abstract_excerpt":"This paper is a Response to Professor J.H.H. Perk's recent Comment (arXiv:1209.0731v1). We point out that the singularities of the reduced free energy {\\beta}f, the free energy per site f and the free energy F of the 3D Ising model differ at {\\beta} = 0. The rigorous proof presented in the Perk's Comment is only for the analyticity of the reduced free energy {\\beta}f, which loses its definition at {\\beta} = 0. Therefore, all of his objections lose the mathematical basis, which are thoroughly disproved. This means that the series expansions cannot serve as a standard for judging the correctness"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3247","kind":"arxiv","version":4},"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"}