Cluster fermionic Ising spin glass model with a transverse field

Abstract

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 J 0 . 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 J 0 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 J 0 when Γ increases until it reaches a quantum critical point at some value of Γ c .