  We investigate the dynamic phase transition in two-dimensional Ising models
whose equilibrium characteristics are influenced by either anisotropic
interactions or quenched defects. The presence of anisotropy reduces the
dynamical critical temperature, leading to the expected result that the
critical temperature approaches zero in the full-anisotropy limit. We show that
a comprehensive understanding of the dynamic behavior of systems with quenched
defects requires a generalized definition of the dynamic order parameter. By
doing so, we demonstrate that the inclusion of quenched defects lowers the
dynamic critical temperature as well, with a linear trend across the range of
defect fractions considered. We also explore if and how it is possible to
predict the dynamic behavior of specific magnetic systems with quenched
randomness. Various geometric quantities, such as a defect potential index, the
defect dipole moment, and the properties of the defect Delaunay triangulation,
prove useful for this purpose.
