Abstract
Abstract We analyze a fermionic Ising spin glass model in the presence of a transverse magnetic field Γ 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 J 0 . 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 n s , values of Γ and J 0 are presented. For instance, the specific heat shows a broad maximum (for n s > 1 ) at a temperature above the freezing temperature T f , which is characterized by the inter-cluster replica symmetry breaking. Phase diagrams T versus Γ show that the critical temperature T f ( Γ ) decreases for any value of n s when Γ increases until it reaches a quantum critical point at some value of Γ c .
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