It is well known  that in two-dimensional (2D) systems with continuous symmetry there is no long range order: for all temperatures, where and . But for continuous Abelian symmetry, a finite-temperature topological phase transition exists and occurs through unbinding of topological point defects. These systems include superfluids, 2D crystalline solids, and XY magnets.
While the static thermodynamic properties are well described by the Kosterlitz--Thouless theory, the dynamical properties are not so well understood. There are variety of quasi-2D magnetic materials, such as , , and others, where the dynamical properties were tested at low frequencies and long wavelengths using inelastic neutron-scattering measurements. More recent experiments show some deviations from existing theories and Monte Carlo simulations. Mertens et al. built a theory which accounts qualitatively well for the behavior of the dynamical form factor above the transition temperature for both the in-plane and out-of-plane correlations. The theory assumes an ideal gas of unbound vortices above the Kosterlitz--Thouless transition temperature and it has as adjustable parameters the root-mean-square vortex velocity and the mean vortex-vortex separation , where is the correlation length. The validity of this theory may depend on the lifetime of free vortices. Though the ideal gas theory supposes infinite lifetime, it will remain approximately correct for a dilute gas too, if the lifetime is greater than the characteristic time which describes their motion .
The purpose of this Letter is to investigate the free vortex lifetime, for which there is no theory, and to consider its implications for the ideal vortex gas theory. The finite lifetime we measure also suggests that creation and annihilation processes may make substantial contributions to dynamic correlations.