Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
  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. 
M. Maksymenko, A. Honecker, R. Moessner, J. Richter, O. Derzhko
cond-mat.stat-mech cond-mat.str-el