Replica symmetry breaking in a fermionic cluster spin glass model in a transverse field - Zimmer F.M.* (2009)
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 J0. 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 ns, values of Γ and J0 are presented. For instance, the specific heat shows a broad maximum (for ns > 1) at a temperature above the freezing temperature Tf, which is characterized by the inter-cluster replica symmetry breaking. Phase diagrams T versus Γ show that the critical temperature Tf (Γ) decreases for any value of ns when Γ increases until it reaches a quantum critical point at some value of Γc. © 2009 Elsevier B.V. All rights reserved.