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It is known that a system which exhibits a half filled lowest flat band andthe localized one-particle Wannier states on the flat band satisfy theconnectivity conditions, is always ferromagnetic. Without the connectivityconditions on the flat band, the system is non-magnetic. We show that this isnot always true. The reason is connected to a peculiar behavior of the bandsituated just above the flat band.

Flat band ferromagnetism without connectivity conditions in the flat band