Competing dynamics in the mixed-spin Ising model with crystal-field interaction

In this work we studied the mixed-spin Ising model with crystal-field interaction and subject to two competing dynamical processes. The model system consists of two interpenetrating sublattices with spins σ=12 and S=1. The spins σ=12 occupy the sites of one sublattice, while the other sublattice is occupied by spins S. The coupling constant between the spins σ and S is of the ferromagnetic type. The system is in contact with a heat bath at a given temperature and, at the same time, subject to an external flow of energy. The contact with the heat bath is simulated by the Glauber dynamics, through single spin-flips, with probability p. The flow of energy is simulated by the process involving a simultaneous flipping of a pair of neighboring spins, with probability (1−p). Both dynamic processes do not conserve the order parameter. In the study of this model we used the dynamical pair approximation and Monte Carlo simulations. We determined the phase diagram in the plane crystal-field D versus temperature T, for all the values of the competition parameter p. We also investigated the appearance of tricritical points in this nonequilibrium thermodynamic system. We also built the phase diagram in the plane crystal-field D versus competition parameter p. In the pair approximation, the phase diagram D×p, presents three phases separated by two transition lines: one continuous transition line between the ferromagnetic (F) and paramagnetic (P) phases, and other first-order transition line between the paramagnetic and antiferromagnetic phases. However, using Monte-Carlo simulations, the same phase diagram exhibits only continuous transition lines.