  A two-dimensional (2D) spin-1/2 antiferromagnetic Heisenberg model with a
specific kind of quenched disorder is investigated, using the first principles
nonperturbative quantum Monte Carlo calculations (QMC). The employed disorder
distribution has a tunable parameter $p$ which can be considered as a measure
of the corresponding randomness. In particular, when $p=0$ the disordered
system becomes the clean one. Through a large scale QMC, the dynamic critical
exponents $z$, the ground state energy densities $E_0$, as well as the Wilson
ratios $W$ of various $p$ are determined with high precision. Interestingly, we
find that the $p$ dependence of $z$ and $W$ are likely to be complementary to
each other. For instance, while the $z$ of $0.4 \le p \le 0.9$ match well among
themselves and are statistically different from $z=1$ which corresponds to the
clean system, the $W$ for $p < 0.7$ are in reasonable good agreement with that
of $p=0$. The technical subtlety of calculating these physical quantities for a
disordered system is demonstrated as well. The results presented here are not
only interesting from a theoretical perspective, but also can serve as
benchmarks for future related studies.
