Dynamical critical transition of an antiferromagnetic Ising model in an oscillating field

The phase diagram of an antiferromagnetic Ising model in a square lattice is studied as a function of temperature and of the frequency of an external uniform oscillating field. The time evolution of the staggered magnetization is obtained through the formalism of the master equation within the dynamical pair approximation. We have shown that the stationary solutions lead to transitions between the antiferromagnetic and paramagnetic phases. The critical field of the transition depends on the competition between the frequencies of the field and that of the spin flipping. We show that for high values of the frequency of the oscillating field the system remains always in a stationary antiferromagnetic state.