Spin glass with $S=1$

A spin glass that differs from the Sherrington–Kirkpatrick model only in the spin's taking three values: $+1$, $0$, $-1$, is investigated. The free energy of the system is obtained in the replica-symmetric approximation, in which the equations for the order parameters are also solved; the entropy at zero temperature is negative. At zero temperature, all spins take values $+1$, $-1$. This makes it possible to calculate the number of metastable states by the method of Edwards and Tanaka. The number is equal to the well-known result for the Sherrington–Kirkpatrick model.