Spin-glass model with uniform biquadratic interactions

We study a spin-1 infinite-ranged Ising spin-glass model with uniform biquadratic exchange interactions. The phase diagram of the model is obtained in the framework of the replica-symmetric solution. For the case of attractive biquadratic interactions the usual spin-glass phase is stabilized at low temperatures, but for the repulsive case, the antiquadrupolar and antiquadrupolar-glaas phases with two-sublattice structure are also possible. We investigate the stability of the replica-symmetric solution and show that the paramagnetic and antiquadrupolar phases are stable, whereas the spin-glass and antiquadrupolar-glass phases are unstable. Parisi's replica-symmetry-breaking procedure is implemented in the neighbourhood of the spin-glass-paramagnetic critical frontier.