{"paper":{"title":"Form factor expansions in the 2D Ising model and Painlev\\'e VI","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Anthony J. Guttmann, Vladimir V. Mangazeev","submitted_at":"2010-02-12T06:56:53Z","abstract_excerpt":"We derive a Toda-type recurrence relation, in both high and low temperature regimes, for the $\\lambda$ - extended diagonal correlation functions $C(N,N;\\lambda)$ of the two-dimensional Ising model, using an earlier connection between diagonal form factor expansions and tau-functions within Painlev\\'e VI (PVI) theory, originally discovered by Jimbo and Miwa. This greatly simplifies the calculation of the diagonal correlation functions, particularly their $\\lambda$-extended counterparts. We also conjecture a closed form expression for the simplest off-diagonal case $C^{\\pm}(0,1;\\lambda)$ where a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.2480","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"}