{"paper":{"title":"Non-Convergent Perturbation Theory and Misleading Inferences about Parameter Relationships: the Case of Superexchange","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other"],"primary_cat":"cond-mat.str-el","authors_text":"D. Psiachos","submitted_at":"2014-07-14T14:23:15Z","abstract_excerpt":"We discuss the well-known three-center cation-anion-cation model for superexchange in insulating transition-metal compounds using limiting expansions for the Anderson-Hubbard model. We find that due to the three interfering energy scales in the model, a limiting expression for the superexchange $J$ for the idealized Mott-Hubbard (M-H) case $t\\ll U\\ll \\Delta$ cannot be formally defined. We further show that no single expansion variable can describe any type of limiting behaviour for superexchange. The well-known $t^4$ expression for M-H insulators, obtained from path-dependent series expansions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3665","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"}