Universality in the three-dimensional random bond quantum Heisenberg antiferromagnet

TL;DR

This study uses large-scale quantum Monte Carlo simulations to analyze the critical behavior of a three-dimensional random bond quantum Heisenberg antiferromagnet, revealing its universality class and precise critical parameters.

Contribution

It provides the first high-precision determination of the Néel temperature and critical exponents for this disordered quantum antiferromagnet, confirming its universality class.

Findings

Critical behavior belongs to the 3D O(3) Heisenberg universality class.

High-precision Néel temperature as a function of coupling ratio.

Confirmation of universality despite quenched disorder.

Abstract

The three-dimensional quenched random bond diluted $(J_1-J_2)$ quantum Heisenberg antiferromagnet is studied on a simple-cubic lattice. Using extensive stochastic series expansion quantum Monte Carlo simulations, we perform very long runs for $L \times L \times L$ lattice up to $L=48$. By employing standard finite-size scaling method, the numerical values of the N\'eel temperature are determined with high precision as a function of the coupling ratio $r=J_2/J_1$. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical $3D$ $O(3)$ Heisenberg universality class.