{"paper":{"title":"Critical correlation functions for the 4-dimensional weakly self-avoiding walk and n-component $|\\varphi|^4$ model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Alexandre Tomberg, Gordon Slade","submitted_at":"2014-12-08T17:10:52Z","abstract_excerpt":"We extend and apply a rigorous renormalisation group method to study critical correlation functions, on the 4-dimensional lattice $\\mathbb{Z}^4$, for the weakly coupled $n$-component $|\\varphi|^4$ spin model for all $n \\geq 1$, and for the continuous-time weakly self-avoiding walk. For the $|\\varphi|^4$ model, we prove that the critical two-point function has $|x|^{-2}$ (Gaussian) decay asymptotically, for $n \\ge 1$. We also determine the asymptotic decay of the critical correlations of the squares of components of $\\varphi$, including the logarithmic corrections to Gaussian scaling, for $n \\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2668","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":""},"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"}