Different processes determine the free vortex lifetime. In general, they can be divided into two classes---pair creation or annihilation and motion of vortices.
Vortices are created or annihilated in pairs due to topological charge conservation. The pair creation process may change the number of free vortices in the system by one or more. For instance, a pair may be created in the neighboring cells of a free vortex, thus making all these vortices bound. A different possibility occurs in a group of four bound vortices(two positive and two negative is the most common case) where two of them annihilate and the rest of them become free.
Vortex motion influences the lifetime in a different way. One possibility is the motion of one or both of two vortices which make up a bound pair. When they move apart from each other they may become free and this leads to creation of one or two more free vortices. The opposite process occurs when a free vortex moves closer to another one, they bind and the number of free vortices decreases.
Simulations show that pair creation and annihilation processes occur more frequently than vortex motion over a distance of one lattice constant. A free vortex almost never travels more than one lattice constant before it becomes a bound one in the cases studied.
In conclusion, we carried out the first study to estimate the lifetime of free vortices in the classical XY model, at two values of the anisotropy parameter . The lifetime increases when approaching from above and reaches for , system size , and . The timescale for decay of the free-vortex number-number correlations was found to be similar to the lifetime. The values of the lifetime and relaxation time for are smaller than those for . Since the existing theory assumes effectively infinite lifetime and its characteristic time scale is larger than , we conclude that the short lifetime should be incorporated in the theory, particularly the processes of vortex creation and annihilation which are the main reason for the short free-vortex lifetime.