Universality in the three-dimensional random bond quantum Heisenberg antiferromagnet

Abstract

The three-dimensional quenched random bond diluted $({J}_{1}\ensuremath{-}{J}_{2})$ 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 an $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ lattice up to $L=48$. By employing a 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 three-dimensional $O(3)$ Heisenberg universality class.