Nonextensive quantum approach to itinerant-electron ferromagnetism: Superstastical method

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 application. 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 electronic specific heat is much increased. This is attributed to enlarged Stoner excitations in the GFD distribution, which is clarified in 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. A problem in applying the superstatistics to nonextensive quantum systems is discussed also. PACS No.: 75.10.Lp, 71.28.+d, 05.30.-d, 75.40.Cx