RS and RSB solutions for SK model with spin-S

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 Thouless (AT) stability conditions for the RS solutions. We find that the AT line exists for all the values of S, including S=∞, and therefore the SK model shows a transition from the RS solution to the RSB solution for all the values of S, including S=∞. It turns out that the properties near T=0 are common for finite S but some of them are not for S=∞.