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

TL;DR

This paper applies one-step replica symmetry breaking to analyze a two-sublattice fermionic Ising spin glass in a transverse field, revealing complex phase transitions and the influence of magnetic fields and quantum effects on magnetic order.

Contribution

It introduces a novel application of one-step RSB to a two-sublattice fermionic spin glass model with transverse field, highlighting asymmetric RSB regions and quantum critical behavior.

Findings

Magnetic field H destroys antiferromagnetic order but favors mixed phases.

Intra-sublattice interactions V increase RSB differences and transition temperatures.

Quantum transverse field Γ suppresses magnetic order but does not restore replica symmetry.

Abstract

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, intra-sublattice 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 discontinue 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 $\Gamma$ 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 intra-sublattice spins couple with disordered interactions.