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Title: Itinerant ferromagnetism in the Hubbard model at finite hole density
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.
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.
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.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: open
Status note: Nagaoka (1966) proved ferromagnetism for a single hole; flat-band models (Mielke, Tasaki) give rigorous ferromagnetism in special lattices.
Posed since: 1966