Growth kinetics of the two-dimensional Ising model with finite cooling rates

We investigate, via spin-flip kinetic Monte Carlo simulations, the entire growth kinetic process of the two-dimensional kinetic Ising model cooled to zero temperature with finite cooling rates. A new slow dynamics, suppressed, and unseen in the instantaneous quench emerges and eventually crosses over to the asymptotic standard coarsening behavior. We present a numerical observation of the excess defect number density that provides direct information on the generated defects due to the critical slowing down. We find that the excess defect density reveals the dynamics of defect generation, which is shown to be in good agreement with the scaling theory pioneered by Kibble and Zurek (KZ). The dynamic spin correlation function reveals that the impulse regime alluded by KZ is characterized by a unique critical coarsening process with the growth law dictated by the Kibble-Zurek mechanism. We determine a new dynamic exponent governing the growth kinetics at the onset times of the zero temperature. The proposed scaling scheme for the excess defect density leads to an analytic expression for this dynamic exponent involving the KZ exponents, indicating the extended influence of the KZ mechanism even down to the kinetics at the onset times of zero temperature. We also perform dynamic simulations of critical heating with finite rates from zero temperature where the power law relaxation (with respect to the inverse cooling rates) of the magnetization can be explained clearly by the KZ exponent.