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

TL;DR

This paper investigates the non-equilibrium annealing process in a 2D XY-model, revealing defect cluster growth, negative transverse stiffness in high-temperature phases, and dynamic scaling of correlation length influenced by disorder.

Contribution

It introduces the concept of inertial growth of vortex clusters and links the disorder-induced shift in vortex friction to dynamic scaling behavior.

Findings

Inertial growth of vortex clusters during coarsening.

Negative transverse stiffness in high-temperature phase.

Dynamic correlation length scales with time and disorder effects.

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.