Abstract
The paramagnetic and diamagnetic susceptibilities of an electron fluid at low but finite temperatures are determined by taking into consideration the free electron, first- and second-order exchange, and ring diagrams, without using the variational method adopted frequently in the past, but rather using a grand-ensemble method. In this method, the grand partition function is evaluated as a function of the magnetic field. The contribution from the ring diagrams is treated accurately with the finite momentum corrections to order ${q}^{4}$ and with the finite temperature corrections to order ${(\mathrm{kT})}^{2}$ to the eigenvalues. The paramagnetic susceptibility, when compared with the data on alkali metals, is found satisfactory. Both the ${r}_{s}$ and temperature dependences of the para- and diamagnetic susceptibilities are determined. When plotted against ${r}_{s}$, the paramagnetic susceptibility increases over the Pauli susceptibility. The diamagnetic susceptibility is also somewhat increased by interaction, although this depends on ${r}_{s}$. The Coulomb energy and the thermal energy are found to counteract in the manifestation of the magnetism. The energy associated with the external magnetic field is evaluated as a function of ${r}_{s}$. In comparison with the case without interaction, the field energy varies more slowly with ${r}_{s}$. The correlation part of the field energy is also determined.
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