Spin-one $p$-spin glass: Exact solution for large $p$

We study the low-temperature properties of the $p$-spin spin glass model in the spin-one (three-state) case for large values of $p$. We show that the one-step replica symmetry-breaking phase is unstable at a very low temperature, and we calculate the explicit boundary of the stability interval, the Gardner temperature, analytically for large values of $p$. This temperature for the spin-one model has the same form of $p$-dependence as in the case of Ising spins (two states). In the one-step replica symmetry-breaking state, a quadrupolar orientational glass coexists with the spin glass and also with a regular quadrupole ordering.