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The quantum critical regime (QCR) of a two-dimensional (2D) disordered and a2D clean dimerized spin-$\frac{1}{2}$ Heisenberg models are studied using thefirst principles nonperturbative quantum Monte Carlo simulations (QMC). Inparticular, the three well-known universal coefficients associated with QCR areinvestigated in detail. While in our investigation we find the obtained resultsare consistent with the related analytic predictions, non-negligible finitetemperature ($T$) effects are observed. Such an influence from $T$ on theproperties of the considered spin systems related to QCR has not been exploredthoroughly before. Moreover, the most striking finding in our study is that thenumerical value for one of the universal coefficients we determine is likely tobe different significantly from the corresponding result(s) established in theliterature. To better understand the sources for the discrepancy observed here,apart from carrying out the associated analytic calculations not consideredpreviously, it will be desirable as well to conduct a comprehensive examinationof the exotic features of QCR for other disordered and clean spin systems thanthose investigated in this study.

Universal quantum criticality at finite temperature for two-dimensional disordered and clean dimerized spin-$\frac{1}{2}$ antiferromagnets