Role of the transverse field in inverse freezing in the fermionic Ising spin-glass model

We investigate the inverse freezing in the fermionic Ising spin-glass (FISG) model in a transverse field $\mathrm{\Gamma }$. The grand canonical potential is calculated in the static approximation, replica symmetry and one-step replica symmetry breaking Parisi scheme. It is argued that the average occupation per site $n$ is strongly affected by $\mathrm{\Gamma }$. As consequence, the boundary phase is modified and, therefore, the reentrance associated with the inverse freezing is modified too.