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

The non-equilibrium annealing of structural disorder in a two-dimensional XY-model leads to coarsening of defects clusters in a cores of spin vortices. We revealed the effect of inertial growth of the clusters in coarsening dynamic regime. The calculated transverse stiffness $rho(p,T)$ of the system in the high-temperature phase $T>T_{rm BKT}(p)$ becomes negative and has described by a power low $rho(p,T) sim T^{-kappa}$ with temperature independent exponent $kappa=kappa(p)$. The dynamical scaling lead 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 spin vortices friction constant $gamma$ induced by annealed disorder.