Mixed-spin ising model with one- and two-spin competing dynamics

In this work we found the stationary states of a kinetic Ising model, with two different types of spins: sigma=1/2 and S=1. We divided the spins into two interpenetrating sublattices, and found the time evolution for the probability of the states of the system. We employed two transition rates which compete between themselves: one, associated with the Glauber process, which describes the relaxation of the system through one-spin flips; the other, related to the simultaneous flipping of pairs of neighboring spins, simulates an input of energy into the system. Using the dynamical pair approximation, we determined the equations of motion for the sublattice magnetizations, and also for the correlation function between first neighbors. We found the phase diagram for the stationary states of the model, and we showed that it exhibits two continuous transition lines: one line between the ferrimagnetic and paramagnetic phases, and the other between the paramagnetic and antiferrimagnetic phases.