Non-equilibrium vortex annealing of structural disorder in Berezinskii-Kosterlitz-Thouless dynamics of the two-dimensional XY-model

The non-equilibrium annealing of structural disorder in a two-dimensional XY-model leads to coarsening of defects clusters in cores of spin vortices. We revealed the effect of "inertial" growth of the clusters in coarsening dynamic regime. The calculated transverse stiffness $\rho(p,T)$ as a function of temperature T and spin concentration p of the system in the high-temperature phase $T>T_{\text{BKT}}(p)$ becomes negative and it is described by a power law $\rho(p,T) \sim T^{-\kappa}$ with temperature-independent exponent $\kappa=\kappa(p)$ . The dynamical scaling leads to the dynamic dependence of the correlation length $\xi \sim (t / \ln^{q} (t/t_{0}))^{1/z}$ which can be explained by a shift of the spin vortices friction constant γ induced by annealed disorder.