We investigate the Sherrington–Kirkpatrick (SK) model with spin-S, including S=∞, in a framework of the replica method. We obtain replica symmetric (RS) solutions and one- and two-step replica symmetry breaking (RSB) solutions by using the Parisi scheme, after verifying de Almeida and...

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...