Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

TL;DR

This paper investigates the complex interplay of antiferromagnetism, spin glass behavior, and superconductivity in a fermionic Ising model with BCS pairing under a transverse magnetic field, revealing rich phase transitions.

Contribution

It introduces a two-sublattice fermionic Ising spin glass model incorporating BCS pairing and analyzes quantum effects of a transverse field on phase transitions.

Findings

AF and SG phases occur at small pairing strength g

Large g favors a pure pairing (PAIR) phase

Quantum fluctuations shift transition lines and tricritical points

Abstract

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field $\Gamma$. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean $J_0$ and standard deviation $J$. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small $g$ ($g$ is the strength of the local superconductor coupling written in units of $J$), while the PAIR phase appears as unique solution for large $g$. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of $\Gamma$.