  An interesting concept that has been underexplored in the context of
time-dependent simulations is the correlation of total magnetization, $C(t)$%.
One of its main advantages over directly studying magnetization is that we do
not need to meticulously prepare initial magnetizations. This is because the
evolutions are computed from initial states with spins that are independent and
completely random. In this paper, we take an important step in demonstrating
that even for time evolutions from other initial conditions, $C(t_{0},t)$, a
suitable scaling can be performed to obtain universal power laws. We
specifically consider the significant role played by the second moment of
magnetization. Additionally, we complement the study by conducting a recent
investigation of random matrices, which are applied to determine the critical
properties of the system. Our results show that the aging in the time series of
magnetization influences the spectral properties of matrices and their ability
to determine the critical temperature of systems.
