Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and is used to derive exact limiting forms (at both long and short wavelengths) for the spin-antisymmetric local-field factor, ${limop}_{\overrightarrow{\omega }\infty }{G}_{-}(\mathbf{q},\omega ).\mathrm{}$ In two dimensions ${limop}_{\overrightarrow{\omega }\infty }{G}_{-}(\mathbf{q},\omega )$ is found to diverge as $1/q$ at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as ${1/q}^2$ in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.

• Received 10 January 2003

DOI:https://doi.org/10.1103/PhysRevB.67.233104