Replica symmetry breaking in a fermionic cluster spin glass model in a transverse field

We analyze a fermionic Ising spin glass model in the presence of a transverse magnetic field ΓΓ within a cluster mean field theory. The model considers a Sherrington–Kirkpatrick type interaction between magnetic moments of clusters with a ferromagnetic intra-cluster coupling J0J0. The spin site operators are written as a bilinear combination of fermionic operators. In these quantum spin glass model, the inter-cluster disorder is treated by using a framework of one-step replica symmetry breaking within the static approximation. The effective intra-cluster interaction is then computed by means of an exact diagonalization method. Results for several cluster size nsns, values of ΓΓ and J0J0 are presented. For instance, the specific heat shows a broad maximum (for ns>1ns>1) at a temperature above the freezing temperature TfTf, which is characterized by the inter-cluster replica symmetry breaking. Phase diagrams T   versus ΓΓ show that the critical temperature Tf(Γ)Tf(Γ) decreases for any value of nsns when ΓΓ increases until it reaches a quantum critical point at some value of ΓcΓc.