{"paper":{"title":"The validity of perturbation theory for the O(N) nonlinear sigma models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"James M. Cline","submitted_at":"2013-03-15T22:52:34Z","abstract_excerpt":"Recently it has been claimed that ordinary perturbation theory (OPT) gives incorrect weak coupling expansions for lattice O(N) non-linear sigma models in the infinite volume limit, and in particular that the two-dimensional non-abelian models are not asymptotically free, contrary to previous findings. Here it is argued that the problem occurs only for one-dimensional infinite lattices, and that in general, OPT gives correct expansions if physical quantities are first computed on a finite lattice, and the infinite volume limit is taken at the end. In one dimension the expansion is sensitive to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3923","kind":"arxiv","version":1},"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"}