  Inspired by the recent results regarding whether the Harris criterion is
valid for quantum spin systems, we have simulated a two-dimensional spin-1/2
Heisenberg model on the square lattice with a specific kind of quenched
disorder using the quantum Monte Carlo (QMC) calculations. In particular, the
considered quenched disorder has a tunable parameter $0\le p \le 1$ which can
be considered as a measure of randomness. Interestingly, when the magnitude of
$p$ increases from 0 to 0.9, at the associated quantum phase transitions the
numerical value of the correlation length exponent $\nu$ grows from a number
compatible with the $O(3)$ result 0.7112(5) to a number slightly greater than
1. In other words, by varying $p$, $\nu$ can reach an outcome between 0.7112(5)
and 1 (or greater). Furthermore, among the studied values of $p$, all the
associated $\nu$ violate the Harris criterion except the one corresponding to
$p=0.9$. Considering the form of the employed disorder here, the above
described scenario should remain true for other randomness if it is based on
the similar idea as the one used in this study. This is indeed confirmed by our
preliminary results stemming from investigating another disorder distribution.
