Inspired by many evidence showing that the Harris criterion could be violated in quantum phase transitions, we study the second-order quantum phase transition of a spin-1/2 antiferromagnetic Heisenberg model with a specific quenched disorder. In particular, various strengths of randomness are considered in our investigation. The studied models will undergo quantum phase transitions by tuning the dimerized-couplings which are close related to the strength of randomness. In addition, the strength of the employed randomness is controlled by a parameter $p$ which is in the range from 0 to 1, where the clean model corresponds to $p=0$.

In this study, we use the stochastic series expansion with efficient loop-update to perform the large-scale quantum Monte Carlo simulation and compute certain physical observables of the model. The critical exponent of the correlation length is evaluated from the finite-size scaling analysis with the Binder ratios as the observables. In order to estimate the statistical uncertainties in a self-consistent way, we analyze the data in the Bayesian inference framework.

In the case of $p=0$, we find that the critical exponent of the correlation length $\nu$ is 0.702(9) which is in reasonably good agreement with the result of $\mathcal{O}(3)$ universality class, and doesn't fulfill the Harris inequality $\nu>2/d$, where $d$ is the spatial dimension and is 2 in this case. Remarkably, while we find that those $\nu$ of $p \le 0.8$ do not fulfill the Harris inequality $\nu > 2/d$, the $\nu$ associated with $p = 0.9$ satisfies such. This interesting phenomenon is not pointed out explicitly before in the literature.

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