Flat band ferromagnetism without connectivity conditions in the flat   band
  It is known that a system which exhibits a half filled lowest flat band and the localized one-particle Wannier states on the flat band satisfy the connectivity conditions, is always ferromagnetic. Without the connectivity conditions on the flat band, the system is non-magnetic. We show that this is not always true. The reason is connected to a peculiar behavior of the band situated just above the flat band. 
Miklos Gulacsi, Gyorgy Kovacs and Zsolt Gulacsi
cond-mat.str-el cond-mat.mes-hall cond-mat.soft