Stable Mean Field Solution of a Short-Range Interacting SO(3) Quantum Heisenberg Spin-Glass

TL;DR

This paper develops a mean-field theoretical framework for a disordered SO(3) quantum Heisenberg spin model with short-range interactions, revealing a phase diagram with antiferromagnetic, spin-glass, and paramagnetic phases and characteristic spin-glass susceptibility behavior.

Contribution

It provides the first mean-field solution for a short-range disordered SO(3) quantum Heisenberg model, analyzing phase stability and magnetic responses.

Findings

Identification of Néel, spin-glass, and paramagnetic phases.

Demonstration of thermodynamic stability via Hessian analysis.

Observation of cusp in magnetic susceptibility at spin-glass transition.

Abstract

We present a mean-field solution for a quantum, short-range interacting, disordered, SO(3) Heisenberg spin model, in which the Gaussian distribution of couplings is centered in an AF coupling $\bar J>0$, and which, for weak disorder, can be treated as a perturbation of the pure AF Heisenberg system. The phase diagram contains, apart from a N\'eel phase at T=0, spin-glass and paramagnetic phases whose thermodynamic stability is demonstrated by an analysis of the Hessian matrix of the free-energy. The magnetic susceptibilities exhibit the typical cusp of a spin-glass transition.