  We investigate the location and nature of the para-ferro transition of
interacting electrons in dispersionless bands using the example of the Hubbard
model on the Tasaki lattice. This case can be analyzed as a geometric
site-percolation problem where different configurations appear with nontrivial
weights. We provide a complete exact solution for the 1D case and develop a
numerical algorithm for the 2D case. In two dimensions the paramagnetic phase
persists beyond the uncorrelated percolation point, and the grand-canonical
transition is via a first-order jump to an unsaturated ferromagnetic phase.
