The influence of size on the dynamic magnetic hysteresis properties and dynamic phase transitions of Fe and \(Fe_3O_4\) 2D-circular nanodisks with varying diameters has been explored in the micromagnetic framework. This investigation is conducted under a sinusoidal dynamic magnetic field along the x-direction by solving the Landau-Lifshitz-Gilbert (LLG) equation with the OOMMF software at zero temperature. The dynamic hysteresis of nanodisks is profoundly impacted by both the frequency and amplitude of the applied external field, along with the particle size. As particle size decreases, there is an observed increase in the frequency values at which the transition to dynamic ordered frequency occurs in Fe nanodisks, whereas a decrease is noted in the transition frequency values of \(Fe_3O_4\) nanodisks.
