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

The quantum critical regime (QCR) of a two-dimensional (2D) disordered and a 2D clean dimerized spin-$\frac{1}{2}$ Heisenberg models are studied using the first principles nonperturbative quantum Monte Carlo simulations (QMC). In particular, the three well-known universal coefficients associated with QCR are investigated in detail. While in our investigation we find the obtained results are consistent with the related analytic predictions, non-negligible finite temperature ($T$) effects are observed. Such an influence from $T$ on the properties of the considered spin systems related to QCR has not been explored thoroughly before. Moreover, the most striking finding in our study is that the numerical value for one of the universal coefficients we determine is likely to be different significantly from the corresponding result(s) established in the literature. To better understand the sources for the discrepancy observed here, apart from carrying out the associated analytic calculations not considered previously, it will be desirable as well to conduct a comprehensive examination of the exotic features of QCR for other disordered and clean spin systems than those investigated in this study.