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

Abstract

The phase diagram of the $p$-spin-interacting spin glass model in a transverse field is investigated in the limit $p\to \infty$ 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 $p\to \infty$ by using the large-$p$ expansion. Since the same approximation is already known to be valid in other phases, we conclude that the obtained phase diagram is exact.

16 pages, 4 figures. another additional author, some amendments

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