Ferromagnetism in flat bands and Pauli-correlated percolation

Flat-band ferromagnetism is an exotic case of itinerant-electron magnetism in a wide class of geometrically frustrated lattices. We develop an exact mapping between the ground state of the many-body problem and a novel site-percolation problem. This allows us to study the ferromagnetic transition using tools from equilibrium statistical physics. In the case of Hubbard model on the Tasaki lattice, we provide a complete and exact solution in 1D and show that for D $>$ 1, the paramagnetic phase persist beyond the uncorrelated percolation point, with a transition in the form of a first-order jump to an unsaturated ferromagnetic phase.