Three-sublattice da Costa–Nobre–Yokoi model with spin S

The two-sublattice da Costa–Nobre–Yokoi (CNY) model of spin S⩾1, where spins on each of two sublattices have uniform biquadratic interactions and random exchange interactions only with spins on the other sublattice, is extended to a model on a lattice with three sublattices. We investigate the three-sublattice CNY model of spin S by using replica symmetry (RS) solutions and de Almeida and Thouless (AT) stability analyses. We find that thermodynamic behaviors of the three-sublattice CNY model of integral S show a two sublattice structure although the model is defined on the lattice with three sublattices; there is a first-order phase transition between the paramagnetic phase and a biquadratic paramagnetic phase and between the spin glass phase and a biquadratic spin glass phase for integral S. On the other hand, the model of half-integral S, including S=∞, does not have any sublattice structure in thermodynamic behaviors.