{"paper":{"title":"Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi-Yau equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"B. M. McCoy, J-M. Maillard, M. Assis, M. van Hoeij, S. Boukraa, S. Hassani","submitted_at":"2011-10-08T07:42:19Z","abstract_excerpt":"We give the exact expressions of the partial susceptibilities $\\chi^{(3)}_d$ and $\\chi^{(4)}_d$ for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau ODEs, and more specifically,\n  $_3F_2([1/3,2/3,3/2],\\, [1,1];\\, z)$ and $_4F_3([1/2,1/2,1/2,1/2],\\, [1,1,1]; \\, z)$ hypergeometric functions. By solving the connection problems we analytically compute the behavior at all finite singular points for $\\chi^{(3)}_d$ and $\\chi^{(4)}_d$. We also give new results for $\\chi^{(5)}_d$. We see in particular, the emergence of a remarkable order-six operator, which is suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1705","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"}