Long-range order versus random-singlet phases in quantum antiferromagnetic systems with quenched disorder

TL;DR

This paper investigates how quenched disorder affects antiferromagnetic systems, revealing conditions under which long-range order remains stable or transitions into a random-singlet phase, emphasizing the role of quantum fluctuations.

Contribution

It introduces a simple model showing the stability conditions of antiferromagnetic order and identifies a nontrivial fixed point related to phase transitions influenced by disorder.

Findings

Long-range order is stable below a critical disorder threshold.

A nontrivial fixed point indicates the transition to a random-singlet phase.

Quantum fluctuations play a key role in stabilizing long-range order.

Abstract

The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to long-range order that is stable unless either the order parameter or the spatial dimensionality exceeds a critical value. The instability of this fixed point corresponds to the system entering a random-singlet phase. The stabilization of long-range order is due to quantum fluctuations, whose role in determining the phase diagram is discussed.