Relaxation dynamics and the free energy near the phase boundary of the 3D kinetic Ising model

We investigate relaxation dynamics along the entire first-order phase transition line by analyzing the time evolution of the free energy landscape in the three-dimensional kinetic Ising model. Near the critical temperature $T_{\rm c}$, the free energy structure is consistent with predictions from Landau-Ginzburg theory. At temperatures far below $T_{\rm c}$, however, fine structures in pre-equilibrium configurations trap random initial states, causing a pronounced delay in equilibration - an effect we identify as ultra-slow relaxation. This phenomenon is characterized by a self-divergence of the relative variance of equilibration times, which we propose as a previously unrecognized hallmark of first-order phase transitions.