{"paper":{"title":"Bounds on $T_c$ in the Eliashberg theory of Superconductivity. I: The $\\gamma$-model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.supr-con","math.MP"],"primary_cat":"math-ph","authors_text":"Boris L. Altshuler, Emil A. Yuzbashyan, Michael K.-H. Kiessling","submitted_at":"2024-08-31T19:43:59Z","abstract_excerpt":"Using the recent reformulation for the Eliashberg theory of superconductivity in terms of a classical interacting Bloch spin chain model, rigorous upper and lower bounds on the critical temperature $T_c$ are obtained for the $\\gamma$ model -- a version of Eliashberg theory in which the effective electron-electron interaction is proportional to $(g/|\\omega_n-\\omega_m|)^{\\gamma}$, where $\\omega_n-\\omega_m$ is the transferred Matsubara frequency, $g>0$ a reference energy, and $\\gamma>0$ a parameter. The rigorous lower bounds are based on a variational principle that identifies $(T_c/g)^\\gamma$ wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.00533","kind":"arxiv","version":2},"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/2409.00533/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"}