Non-equilibrium vortex annealing of structural disorder in the critical relaxation of diluted two-dimensional XY-model

The study of the effects of aging in the non-equilibrium critical relaxation of a two-dimensional XY-model with a non-equilibrium vortex annealing of structural disorder has been carried out. Two-time dynamic dependencies of the spin-spin and defect-defect autocorrelation functions C_SS(t, t_w) and C_DD(t, t_w) are obtained for the entire Berezinskii low-temperature phase T < T_BKT(p), for a wide range of waiting times t_w and spin concentrations p. Near the BKT phase transition point T_BKT(p), the dynamic dependencies C_DD(t, t_w) become uniform with time. However, with a decrease in temperature in the low-temperature phase T < T_BKT(p), this relaxation uniformity breaks down, and CDD(t, t_w) does not exhibit canonical aging properties. The formation of a declining family of dynamical scaling curves is clearly observed at large observation times t − t_w which may indicate the presence of an asymptotic scaling dependence of CDD(t, t_w. (paper)