The Quantum Random Energy Model as a Limit of p-Spin Interactions

We consider the free energy of a mean-field quantum spin glass described by a $p$-spin interaction and a transversal magnetic field. Recent rigorous results for the case $p= \infty$, i.e. the quantum random energy model (QREM), are reviewed. We show that the free energy of the $p$-spin model converges in a joint thermodynamic and $p \to \infty$ limit to the free energy of the QREM.