 93141 Andreas Mielke , Hal Tasaki
 Ferromagnetism in the Hubbard Model
 Examples from Models with
Degenerate SingleElectron Ground States
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May 21, 93

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Abstract. Whether spinindependent Coulomb interaction can be the origin of
a realistic ferromagnetism in an itinerant electron system has
been an open problem for a long time.
Here we study a class of Hubbard models on decorated lattices,
which have a special property that the corresponding
singleelectron Schr\"{o}dinger
equation has $N_{\rm d}$fold degenerate ground states.
The degeneracy $N_{\rm d}$ is proportional to the total number of
sites $\abs{\Lambda}$.
We prove that the ground states of the models exhibit
ferromagnetism when the electron filling factor is not more than
and sufficiently close to $\rho_0=N_{\rm d}/(2\abs{\Lambda})$, and
paramagnetism when the filling factor is
sufficiently small.
An important feature of the present work is that it provides
examples of three dimensional itinerant electron systems which are
proved to exhibit ferromagnetism in a finite range of the electron
filling factor.
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