Degeneracy and quantum effects in the Hubbard model

The thermodynamics of the degenerate-band Hubbard model is investigated using the two-field static approximation to the functional-integral method. It is shown that the previous calculation scheme based on the results for the single-band model includes the effects of orbital degeneracy and Hund’s-rule coupling. Emphasis is put on the role of the degeneracy and the quantum effects involved in the two-field method. A new expression for the amplitude of the local moment (〈${\mathrm{m}}^2$〉${)}^{1/2}$ is derived from the free energy. The quantum effects on the amplitude (〈${\mathrm{m}}^2$〉${)}^{1/2}$ are examined in detail as a function of the degeneracy and the Coulomb and exchange parameters. Theoretical values for (〈${\mathrm{m}}^2$〉${)}^{1/2}$ are 3.3${\mu }_B$ for Fe, 1.4${\mu }_B$–1.7${\mu }_B$ for Ni, and 2.8${\mu }_B$ for Cr at $T_C$. The results raise an objection to the experimental values obtained by means of neutron scattering: 1.5${\mu }_B$ for Fe, 0.9${\mu }_B$ for Ni, and 0.28${\mu }_B$ for Cr.