Magnetic order in itinerant electron systems arises from the on-site repulsion interaction between electrons, U , due to local moment formation and their coupling via the exchange energy. Therefore, the moment formation, e.g. in the single-band Hubbard model on the square lattice, is weakened when a fraction x of U is randomly set to zero, exhibiting an upper bound dilution limit as the classical percolation threshold of the lattice, x (perc,sq) c . In this paper, we study dilute magnetism in flat band systems, namely in the Hubbard model on a 'Lieb' lattice. Interestingly, we show that magnetic order persists to x almost twice as large as the classical percolation threshold for the lattice, thus emphasizing the central role of electron itinerancy to the magnetic response. The analysis of the orbital-resolved order parameters reveals that the contribution of the four-fold coordinated 'd' sites to magnetism is dramatically affected by dilution, while the localized 'p' states of the flat band provide the dominant contribution to long-range correlations. We also examine the transport properties, which suggest the existence of an insulator-to-metal transition in the same range of the critical magnetic dilution.
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