Ferromagnetism in a Hubbard model for an atomic quantum wire: a   realization of flat-band magnetism from even-membered rings
  We have examined a Hubbard model on a chain of squares, which was proposed by Yajima et al as a model of an atomic quantum wire As/Si(100), to show that the flat-band ferromagnetism according to a kind of Mielke-Tasaki mechanism should be realized for an appropriate band filling in such a non-frustrated lattice. Reflecting the fact that the flat band is not a bottom one, the ferromagnetism vanishes, rather than intensified, as the Hubbard U is increased. The exact diagonalization method is used to show that the critical value of U is in a realistic range. We also discussed the robustness of the magnetism against the degradation of the flatness of the band. 
R. Arita, K. Kuroki, H. Aoki, A. Yajima, M. Tsukada, S. Watanabe, M.   Ichimura, T. Onogi and T. Hashizume