{"paper":{"title":"Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. III. Shock and rarefaction waves in RG flows reveal limitations of the $N\\rightarrow\\infty$ limit in $O(N)$-type models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th","physics.comp-ph","physics.flu-dyn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Adrian Koenigstein, Martin J. Steil","submitted_at":"2021-08-09T13:42:12Z","abstract_excerpt":"Using an $O(N)$-symmetric toy model QFT in zero space-time dimensions we discuss several aspects and limitations of the $\\frac{1}{N}$-expansion. We demonstrate, how slight modifications in a classical UV action can lead the $\\frac{1}{N}$-expansion astray and how the infinite-$N$ limit may alter fundamental properties of a QFT. Thereby we present the problem of calculating correlation functions from two totally different perspectives: First, we explicitly analyze our model within an $\\frac{1}{N}$-saddle-point expansion and show its limitations. Secondly, we picture the same problem within the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.04037","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/2108.04037/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"}