Dynamic Behavior ofS=12XYModel on Cubic Lattices. I. Molecular-Field Approximation

The time behavior of the spin operator $S_{\overrightarrow{\mathrm{k}}}^x\mathrm{}\left(t\right)\mathrm{}$ in the $\mathrm{XY}$ model is studied by a perturbative method. The zeroth order, which truncates a certain zero-time commutator, is shown to be equivalent to a molecular-field approximation. An analytic expression for the dynamic form factor is then obtained which satisfies basic sum rules. Through the fluctuation-dissipation theorem the dynamic susceptibility and other related physical quantities are also given. Within this zeroth-order approximation there exists a high-frequency collective mode at $q^{\frac{1}{2}}J$ This mode is undamped and is similar to the plasmon.