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

TL;DR

This paper maps out the phase diagram of a complex p-spin spin glass model with ferromagnetic bias and a transverse field in the infinite-p limit, revealing four distinct phases and confirming the static approximation's validity.

Contribution

It provides an exact phase diagram for the p-spin-interacting spin glass with ferromagnetic bias in the infinite-p limit using the replica method and static approximation.

Findings

Identifies four phases: quantum paramagnetic, classical paramagnetic, ferromagnetic, and spin-glass.

Confirms the static approximation's validity in all phases in the infinite-p limit.

Establishes the phase diagram as exact due to the large-p expansion analysis.

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.