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We consider nearly-flat-band Hubbard models of a ferromagnet, that is themodels that are weak perturbations of those flat-band Hubbard models whoseground state is ferromagnetic for any nonzero strength $U$ of the Hubbardrepulsion. In contrast to the flat-band case, in the nearly-flat-band case theground state, being paramagnetic for $U$ in a vicinity of zero, turns into aferromagnetic one only if $U$ exceeds some nonzero threshold value $U_{th}$. Weaddress the question whether $U_{th}$ of the considered models is in a physicalrange, therefore we attempt at obtaining possibly good estimates of thethreshold value $U_{th}$. A rigorous method proposed by Tasaki is extended andthe resulting estimates are compared with small-system, finite-size scalingresults obtained for open- and periodic-boundary conditions. Contrary tosuggestions in literature, we find the latter conditions particularly usefulfor our task.

Estimating the Hubbard repulsion sufficient for the onset of nearly-flat-band ferromagnetism