Using a Monte Carlo simulation, the effect of external field, temperature, system’s dimensions and interaction of non-nearest neighbors on the relaxation time and critical indices of an antiferromagnetic-to-ferromagnetic phase transition is investigated taking into account nonmagnetic impurities within a modified, onedimensional, nanosized Ising model. It is shown that the non-equilibrium processes taking place in the magnetic material could be classified as fast and slow, whose velocities differ by more than a thousand times. In the case of fast processes, metastable (including ferromagnetic) states (observed experimentally) are the first to form, while in the case of slow processes the system transits into a stable state. The behavior of the dynamic critical exponent (z) and static correlation-length critical exponent (ν) is revealed for the model of a 1D ferromagnetic for the case of arbitrary concentrations of nonmagnetic impurities.