One-step replica symmetry breaking solution for a highly asymmetric two-sublattice fermionic Ising spin-glass model in a transverse field

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 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 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, 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.