Nonextensive quantum method for itinerant-electron ferromagnetism: Fractorization approach

TL;DR

This paper introduces a nonextensive quantum approach using a generalized Fermi-Dirac distribution to analyze itinerant-electron ferromagnetism, revealing how nonextensivity affects magnetic and thermodynamic properties.

Contribution

The study derives a GFD distribution within superstatistics and applies it to the Hubbard model, highlighting the impact of nonextensivity on ferromagnetic properties.

Findings

Magnetic moment's temperature dependence becomes more pronounced with increasing |q-1|.

Low-temperature specific heat significantly increases with nonextensivity.

Enlarged Stoner excitations explain the effects of nonextensivity.

Abstract

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.