  We investigate the para-ferro transition of the repulsive SU($N$) Hubbard
model on one- and two-dimensional Tasaki lattices. Under certain restrictions
for constructing localized many-particle ground states of flat-band
ferromagnetism, the quantum strongly correlated electrons model is mapped to a
classical statistical geometric site-percolation problem, where the nontrivial
weights of different configurations must be considered. We prove rigorously the
para-ferro transition for the SU($N$) Hubbard model on one-dimensional Tasaki
lattice by transfer-matrix method, and numerically verify it for the model with
symmetries up to SU($10$). In two dimensions, we numerically investigate the
phase transition of SU($3$), SU($4$) and SU($10$) Hubbard models by Metropolis
Monte Carlo simulation. And we find the critical density exceeds that of
standard percolation, and it increases with spin degrees of freedom, implying
that the effective repulsive interaction becomes stronger for larger $N$. We
further rigorously prove the flat-band ferromagnetism of the SU$(N)$ Hubbard
model, when the number of particles $N_e$ equals to the degeneracy $N_d$ of the
lowest band in the single-particle energy spectrum.
