{"paper":{"title":"The Ising Partition Function: Zeros and Deterministic Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.CC","cs.DM","math.CO"],"primary_cat":"cs.DS","authors_text":"Alistair Sinclair, Jingcheng Liu, Piyush Srivastava","submitted_at":"2017-04-21T11:46:22Z","abstract_excerpt":"We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs that is valid over the entire range of parameters $\\beta$ (the interaction) and $\\lambda$ (the external field), except for the case $\\vert{\\lambda}\\vert=1$ (the \"zero-field\" case). A randomized algorithm (FPRAS) for all graphs, and all $\\beta,\\lambda$, has long been known. Unlike most other deterministic approximation algorithms for problems in statistical "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.06493","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"}