Quantum criticality at finite temperature for two-dimensional JQ₃ models on the square and the honeycomb lattices

We study the quantum criticality at finite temperature for three two-dimensional (2D) JQ₃ models using the first principles quantum Monte Carlo calculations (QMC). In particular, the associated universal quantities are obtained, and their inverse temperature dependence is investigated. The considered models are known to have quantum phase transitions from the Néel order to the valence-bond solid, and these transitions are shown to be possibly of second order for two of the studied models, with the remaining one being of first order. When the temperature dependence of the studied universal quantities is considered, we observe substantial differences between the two models likely possessing second-order phase transitions and the remaining model. Moreover, by using the associated data from both the models that may have continuous transitions, good data collapses are obtained for a number of the considered universal quantities. The findings presented here provide numerical evidence to support particular results established in the literature regarding the nature of the phase transitions of these JQ₃ models, and can be employed as useful criterions to distinguish second-order phase transitions from first-order ones for the exotic criticalities of the JQ-type models.