The one-step replica symmetry breaking (RSB) is used to study a two-sublattice fermionic infinite-range Ising spin-glass (SG) model in a transverse field $\ensuremath{\Gamma}$. The problem is formulated in a Grassmann path integral formalism within the static approximation. In this model, a parallel magnetic field
H breaks the symmetry of the sublattices. It destroys the antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase
(SG+AF) characterizing an asymmetric RSB region. In this region, intrasublattice disordered interactions
V increase the difference between the RSB solutions of each sublattice. The freezing temperature shows a higher increase with
H when
V enhances. A discontinuous phase transition from the replica symmetry (RS) solution to the RSB solution can appear with the presence of an intrasublattice ferromagnetic average coupling. The $\ensuremath{\Gamma}$ field introduces a quantum spin-flip mechanism that suppresses the magnetic orders leading them to quantum critical points. Results suggest that the quantum effects are not able to restore the RS solution. However, in the asymmetric RSB region, $\ensuremath{\Gamma}$ can produce a stable RS solution at any finite temperature for a particular sublattice while the other sublattice still presents RSB solution for the special case in which only the intrasublattice spins couple with disordered interactions.
In the present work, a fermionic infinite-range Ising spin glass (SG) model with a transverse field Γ is studied. The model is analyzed in a one-lattice structure (quantum SG) and in a two-sublattice structure (SG/antiferromagnetism (AF) competition). In these two cases, the exchange interactions are random variables that follow Gaussian probability distributions (SK interactions). For the two-sublattice model, spins of distinct sublattices can couple with an SK-type interaction with an AF average. For a general case of this model, the disordered interactions can also occur with spins of same sublattices. The problem is formulated in a Grassmann path integral formalism within the static ansatz. The replica method is applied to treat the disorder, in which the replica symmetry (RS) and one-step replica symmetry breaking (1P-RSB) approximations are used. The one-lattice model results provide evidences that the 1S-RSB can be used to improve the physical description of the ordered quantum SG phase treated by the replica method. In the two-sublattice model, a parallel magnetic field H breaks the symmetry of the sublattices. It destroys the antiferromagnetic (AF) order, but it can favor the nonergodic mixed phase (SG+AF) characterizing an asymmetric RSB region. In this region, intra-sublattice disordered interactions V increase the difference between the RSB solutions of each sublattice. The freezing temperature (Tf ) shows a higher increase with H when V enhances. A discontinuous phase transition from the replica symmetry (RS) solution to the RSB solution can appear with the presence of an intra-sublattice ferromagnetic average coupling. The Γ field introduces a quantum spin flip mechanism that suppresses the magnetic orders leading them to quantum critical points. Results suggest that the quantum effects are not able to restore the RS solution. Therefore, the presence of both fields, Γ and H, produces effects that are in competition on Tf for instance. However, in the asymmetric RSB region, Γ can produce a stable RS solution at any finite temperature for a particular sublattice while the other sublattice still presents RSB solution for the special case in which only the intra-sublattice spins couple with disordered interactions.