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 $T>T_{\mathrm{BKT}}(p)$ 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.

7 pages, 8 figures, supplementary materials

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