Phase diagrams and magnetization curves of the mixed Ashkin–Teller model including metastable and unstable states

We investigate the magnetic properties of a mixed Ashkin–Teller model (spin-1/2 and spin-1) in a square lattice, under the effect of a crystal field, using the mean-field theory. Phase diagrams, magnetizations and free energy curves are presented. Besides the stable states of the order parameters, we also obtain the metastable and unstable states, which are shown in the phase diagrams and magnetization curves. The classification of the stable, metastable and unstable states is made by comparing their free-energy values. Graphic abstract