Memory effects in the nonequilibrium critical behavior of the two-dimensional $XY$ model in the low-temperature Berezinskii phase

The Monte Carlo study of nonequilibrium memory effects in the two-dimensional pure and structurally disordered $XY$ model in the low-temperature Berezinskii phase has been performed. Features of the correlation between memory and aging effects have been demonstrated. A qualitatively novel phenomenon for memory effects has been revealed: dynamic curves of the autocorrelation function in the thermal cycling time interval tend to the dynamic curves with the initial temperature. A unique implementation of memory effects has been demonstrated at both cooling and heating cycling of the system under the condition that cooling and heating temperatures are in the low-temperature Berezinskii phase. The influence of structural disorder on memory effects has been analyzed. It has been found that they are enhanced in the structurally disordered system owing to the enhancement of aging effects.