{"paper":{"title":"Numerical Accuracy of the Derivative-Expansion-Based Functional Renormalization Group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Andrzej Chlebicki","submitted_at":"2024-04-29T13:57:16Z","abstract_excerpt":"We investigate the precision of the numerical implementation of the functional renormalization group based on extracting the eigenvalues from the linearized RG transformation. For this purpose, we implement the LPA and $O(\\partial^2)$ orders of the derivative expansion for the three-dimensional $O(N)$ models with $N~\\in~\\{1,2,3\\}$. We identify several categories of numerical error and devise simple tests to track their magnitude as functions of numerical parameters. Our numerical schemes converge properly and are characterized by errors of several orders of magnitude smaller than the error bar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.18707","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.18707/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}