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 [Formula: see text]-spin interaction and a transversal magnetic field. Recent rigorous results for the case [Formula: see text], i.e. the quantum random energy model (QREM), are reviewed. We show that the free energy of the [Formula: see text]-spin model converges in a joint thermodynamic and [Formula: see text] limit to the free energy of the QREM.