{"paper":{"title":"Long-range multi-scalar models at three loops","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"hep-th","authors_text":"Dario Benedetti, Kenta Suzuki, Razvan Gurau, Sabine Harribey","submitted_at":"2020-07-09T07:25:38Z","abstract_excerpt":"We compute the three-loop beta functions of long-range multi-scalar models with general quartic interactions. The long-range nature of the models is encoded in a kinetic term with a Laplacian to the power $0<\\zeta<1$, rendering the computation of Feynman diagrams much harder than in the usual short-range case ($\\zeta=1$). As a consequence, previous results stopped at two loops, while six-loop results are available for short-range models. We push the renormalization group analysis to three loops, in an $\\epsilon=4\\zeta-d$ expansion at fixed dimension $d<4$, extensively using the Mellin-Barnes r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.04603","kind":"arxiv","version":3},"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/2007.04603/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"}