Cluster fermionic Ising spin glass model with a transverse field

The fermionic Ising spin glass (SG) model in the presence of a transverse magnetic field Γ is studied within a cluster mean field theory. The model considers an infinite-range interaction among magnetic moments of clusters with a short-range ferromagnetic intracluster coupling J0. The spin operators are written as a bilinear combination of fermionic operators. In this quantum SG model, the intercluster disorder is treated by using a framework of one-step replica symmetry breaking (RSB) within the static approximation. The effective intracluster interaction is then computed by means of an exact diagonalization method. Results for several values of cluster size ns, Γ and J0 are presented. For instance, the specific heat can show a broad maximum at a temperature T∗ above the freezing temperature Tf, which is characterized by the intercluster RSB. The difference between T∗ and Tf is enhanced by Γ, which suggests that the quantum effects can increase the ratio T∗/Tf. Phase diagrams (T versus Γ) show that the critical temperature Tf(Γ) decreases for any values of ns and J0 when Γ increases until it reaches a quantum critical point at some value of Γc.