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

Abstract: 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.