{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4c0956bf5e9b6f247f7453b060eb8719cce2c5b3e0a36a96e851a2e58beb14cd","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"9cafe2bcd253b601c70116d940cc3dd31ef1e585c52fc52856f1c0be43c801ef","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"mathph.fermi-liquids-bcs.nagaoka-finite-density","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"With infinitely strong repulsion and exactly one missing electron, the Hubbard model is proven to be a ferromagnet. Whether this survives for a small but finite fraction of missing electrons is unknown.","posed_since":"1966","precise":"Hubbard model at $U = \\infty$ on $Z^{2}$ or $Z^{3}$, electron density $1 - \\delta$ with hole density $\\delta > 0$ small, thermodynamic limit. Prove or disprove that the ground state has total spin $S_{\\mathrm{tot}}$ of order $N$ (saturated or partial ferromagnetism). Answer: yes or no with proof.","problem_ref":null,"references":"","settled_by":"A proof of a ground state with $S_{\\mathrm{tot}}$ proportional to $N$, or a variational state with lower energy and $S_{\\mathrm{tot}} = o(N)$, valid in the thermodynamic limit.","status_note":"Nagaoka (1966) proved ferromagnetism for a single hole; flat-band models (Mielke, Tasaki) give rigorous ferromagnetism in special lattices.","title":"Itinerant ferromagnetism in the Hubbard model at finite hole density","topic_ref":"092ec16641325783d3e30e41c35811e9c4984811735d26f9a5dda60705ccb883"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"0b7ad28e1fc6882ed55689123ded8ffdc2ec95d6bf4854de156779a673c883a1","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"9342069c0cf0561c036d39edffd1f790aeb3206f35a0a43a30465aeae2ba3e1d","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"htQy0ihS173acNMYw8Sg2IRiw7YTNaKyX6W9T86sdUFSIjGEffUwwRWI0E7QVhvJixBN5NdH_KDWeWu3_-QzAQ"},"schema":"pubphys.envelope/1"},"record_hash":"0b7ad28e1fc6882ed55689123ded8ffdc2ec95d6bf4854de156779a673c883a1","leaf_index":1615}