One-step replica symmetry breaking solution for fermionic Ising spin glass in a transverse field

TL;DR

This paper develops a one-step replica symmetry breaking solution for fermionic Ising spin glasses in a transverse field, incorporating a variational parameter for the Parisi block size, revealing RSB persists at zero temperature due to quantum fluctuations.

Contribution

It extends previous static ansatz models by treating the Parisi parameter as a variational quantity, providing new insights into quantum fluctuation effects at zero temperature.

Findings

RSB persists as temperature approaches zero

Quantum fluctuations drive the RSB at low temperatures

The variational approach refines the understanding of spin glass behavior

Abstract

The fermionic Ising spin glass models in a transverse field are investigated in a Grassmann path integral formalism. The Parisi's scheme of one-step replica symmetry breaking (RSB) is used within the static ansatz. This formalism has already been applied in a theory in which $m$ (Parisi's block-size parameter) is taken as a constant (PRB 72, 014447 (2005)). Now, it is extended to consider $m$ as a variational parameter. In this case, the results show that RSB is present when $T\to0$, in which the system is driven by quantum fluctuations.