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 (QMCs). The employed disorder distribution has a tunable parameter p which can be considered as a measure of randomness (p=0 correponds to the clean model). Through large-scale QMCs, the dynamic critical exponents z, the ground-state energy densities E0, and the Wilson ratios W of various p are determined with high precision. Interestingly, we find that the p dependencies of z and W are likely to be complementary to each other. For instance, while the z values of 0.4=p=0.9 match well among themselves and are statistically different from that of p=0, the W values for p<0.7 are in reasonably good agreement with W~0.1243 of the clean case. Surprisingly, our study indicates that a threshold of randomness, pW, associated with W exists. In particular, beyond this threshold the magnitude of W grows with p. This is somehow counterintuitive since one expects the spin correlations should diminish accordingly. Similarly, there is a threshold pz related to z after which a constant value is obtained for z. The results presented here are not only interesting from a theoretical perspective but also can serve as benchmarks for future related studies.
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