Theory of the dynamic spin response function near the Kosterlitz-Thouless transition

The pioneering work of Ambegaokar, Halperin, Nelson, and Siggia on dynamical phenomena in superfluid films near the Kosterlitz-Thouless transition is formulated in a more systematic way in the context of the classical two-dimensional (2D) XY model. Specifically, we extend the discussion of Nelson and Fisher on spin dynamics to include the effect of the vortices. The coupled equations of motion for the spin-wave and vortex fields are derived from a Lagrangian analogous to that used in classical electrodynamics of a continuous medium. In the electromagnetic analogy, the spin waves (or third sound) correspond to transverse photons, the renormalization effects of the bound vortex pairs entering through the transverse dielectric function ${\epsilon }_{\perp }$(q,ω) of the equivalent 2D neutral Coulomb gas. The relation between our results for the dynamic response functions and previous work on static response functions (in which the spin-wave–vortex coupling is apparently ignored) is clarified by noting the distinction between the bare (${\mathrm{theta}}_0$) and the renormalized (theta=${\mathrm{theta}}_0$/${\epsilon }_{\perp }$) spin-wave fields.