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Even for a perturbatively small fixed point coupling $\\lambda_*$, standard perturbation theory breaks down for sufficiently large $\\lambda_*n$. Treating $\\lambda_* n$ as fixed for small $\\lambda_*$ we show that $\\Delta_{\\phi^n}$ can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in $$ \\Delta_{\\phi^n}=\\frac{1}{\\lambda_*}\\Delta_{-1}(\\lambda_* n)+\\Del"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1909.01269","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-09-03T16:05:05Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","hep-ph"],"title_canon_sha256":"40ea44b792c1e9b656df7ca79588e60c00831fc248b8fca0cee998133e78ef3a","abstract_canon_sha256":"fa7bc5035b680588850cfbc0a045bdbf743e5ecd9606cbf1c29b61b74a9932aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:07:50.411023Z","signature_b64":"uEv47drPq2azfc8f2FGHAlTpo5RPgDAS8pbnBrSXNgOlMZhIIp1UCkQjDGkXpcxUmzxrcqybtoixFVx9kkZVCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb2eb723e4413307f331f56459882d0759e8957034f600233ef94ded77b1ec71","last_reissued_at":"2026-07-05T01:07:50.410548Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:07:50.410548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Epsilon Expansion Meets Semiclassics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","hep-ph"],"primary_cat":"hep-th","authors_text":"Alexander Monin, Gabriel Cuomo, Gil Badel, Riccardo Rattazzi","submitted_at":"2019-09-03T16:05:05Z","abstract_excerpt":"We study the scaling dimension $\\Delta_{\\phi^n}$ of the operator $\\phi^n$ where $\\phi$ is the fundamental complex field of the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\\varepsilon$. 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