  Magnetic and thermodynamical properties of itinerant-electron (metallic)
ferromagnets described by the Hubbard model have been discussed with the use of
the generalized Fermi-Dirac (GFD) distribution for nonextensive quantum
systems. We have derived the GFD distribution within the superstatistics, which
is equivalent to that obtained by the maximum-entropy method to the Tsallis
entropy with the factorization approimation. By using the Hartree-Fock
approximation to the electron-electron interaction in the Hubbard model, we
have calculated magnetic moment, energy, specific heat and Curie-Weiss-type
spin susceptibility, as functions of the temperature and entropic index $q$
expressing the degree of the nonextensivity: $q=1.0$ corresponds to the
Boltzmann-Gibbs statistics. It has been shown that with increasing the
nonextensivity of $| q-1 |$, the temperature dependence of magnetic moment
becomes more significant and the low-temperature electronic specific heat is
much increased. This is attributed to enlarged Stoner excitations in the GFD
distribution, which is elucidated by an analysis with the use of the
generalized Sommerfeld expansion. We discuss the difference and similarity
between the effects of the nonextensivity on metallic and insulating
ferromagnets.
