title: Flat-band ferromagnetism as a Pauli-correlated percolation problem.
abstract: 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 one-dimensional case and develop a numerical algorithm for the two-dimensional 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.
authors.affiliation: Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, L'viv, Ukraine.
authors.forename: M
authors.initials: M
authors.lastname: Maksymenko
authors.forename: A
authors.initials: A
authors.lastname: Honecker
authors.forename: R
authors.initials: R
authors.lastname: Moessner
authors.forename: J
authors.initials: J
authors.lastname: Richter
authors.forename: O
authors.initials: O
authors.lastname: Derzhko