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

Abstract

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 CSS (t,tw) and CDD (t,tw) are obtained for the entire Berezinskii low-temperature phase T < TBKT(p), for a wide range of waiting times tw and spin concentrations p. Near the BKT phase transition point TBKT (p), the dynamic dependencies CDD(t,tw) become uniform with time. However, with a decrease in temperature in the low-temperature phase T < TBKT (p), this relaxation uniformity breaks down, and CDD(t,tw) does not exhibit canonical aging properties. The formation of a declining family of dynamical scaling curves is clearly observed at large observation times t – tw which may indicate the presence of an asymptotic scaling dependence of CDD (t, tw).