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 n_s, Γ and J₀ are presented. For instance, the specific heat can show a broad maximum at a temperature T^∗ above the freezing temperature T_f, which is characterized by the intercluster RSB. The difference between T^∗ and T_f is enhanced by Γ, which suggests that the quantum effects can increase the ratio T^∗/T_f. Phase diagrams (T versus Γ) show that the critical temperature T_f(Γ) decreases for any values of n_s and J₀ when Γ increases until it reaches a quantum critical point at some value of Γ_c.