Replica symmetry breaking solution for two-sublattice fermionic Ising spin glass models in a transverse field

Abstract The one-step replica symmetry breaking is used to study the competition between spin glass (SG) and antiferromagnetic order (AF) in two-sublattice fermionic Ising SG models in the presence of a transverse Γ and a parallel H magnetic fields. Inter- and intra-sublattice exchange interactions following Gaussian distributions are considered. The problem is formulated in a Grassmann path integral formalism within the static ansatz. Results show that H favors the non-ergodic mixed phase (AF+SG) and it destroys the AF. The Γ suppresses the magnetic orders, and the intra-sublattice interaction can introduce a discontinuous phase transition.