Domain Wall Pinning and Frequency-Dependent Phase Boundaries in the Driven 2D Ising Model

The dynamic phase transitions of periodically driven ferromagnets present a complex interplay between internal relaxation dynamics and external driving forces. In this study, a highly optimized Metropolis-Hastings Monte Carlo simulation is developed to model a two-dimensional Ising ferromagnet subjected to an oscillating magnetic field. Following exact thermodynamic validation of the static critical exponent ($\gamma/\nu \approx 1.75$), the system is pushed out of equilibrium to investigate two competing mechanisms of phase disruption: structural spatial disorder and temporal frequency variation. Computational results demonstrate that quenched non-magnetic impurities act as localized pinning centers for expanding domain walls, fundamentally "softening" the material and drastically shrinking the dynamically ordered parameter space. Conversely, scaling the driving frequency outpaces localized spin relaxation, effectively bypassing the chaotic limit cycle and expanding the dynamically ordered phase. This offers a mathematical profile of non-equilibrium phase boundaries in disordered magnetic lattices.