The infinite-range two-real-Ising replicas spin glass

A spin-glass model, with two Ising coupled systems (real replicas), is investigated in the limit of infinite-range interactions, through the replica method. Besides the Ising representation, the model is also considered as a discrete two-component four-state clock spin glass. The phase diagram of the model is obtained, within the replica-symmetry approximation, exhibiting a collinear spin-glass phase, i.e., no transverse four-state clock ordering. The order parameter conjugated to the coupling field presents a discontinuity along the spin-glass phase, when the field is reversed. The validity limits of the replica-symmetry solution are analysed.