Replica symmetry breaking solution for the fermionic Ising spin-glass and the Ghatak-Sherrington model

We solve the fermionic version of the Ising spin glass for arbitrary filling mu and temperature T taking into account replica symmetry breaking. Using a simple exact mapping from mu to the anisotropy parameter D, we also obtain the solution of the S = 1 Sherrington-Kirkpatrick model. An analytic expression for T = 0 gives an improved critical value for the first-order phase transition. We revisit the question of stability against replica-diagonal fluctuations and find that the appearance of complex eigenvalues of the Almeida-Thouless matrix is not an artefact of the replica-symmetric approximation.