Kinetic phase transition in the semi-infinite Ising model under an oscillating field

The kinetics of the semi-infinite Ising model, in the presence of a time-dependent oscillating external field, is studied within the framework of the mean-field approach. We use the Glauber-type stochastic dynamics to describe the time evolution of this system. In addition to the well-known phase transitions (ordinary, extraordinary, and surface phase transitions) in the equilibrium case, a dynamical phase appears in which the bulk orders, whereas the surface is disordered. Consequently, a variety of phase diagrams is obtained. Furthermore, the system exhibits dynamical first-order phase transition. The magnetizations and phase space trajectories are given and discussed.