Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit

The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p\to \mathrm{\infty }$ under the presence of ferromagnetic bias. Using the replica method and the static approximation, we show that the phase diagram consists of four phases: Quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass phases. We also show that the static approximation is valid in the ferromagnetic phase in the limit $p \to \infty$byusingthelarge-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.