  We have investigated the quantum phase transitions in the ground states of
several critical systems, including transverse field Ising and XY models as
well as XY with multiple spin interactions, XXZ and the collective system
Lipkin-Meshkov-Glick models, by using different quantumness measures, such as
entanglement of formation, quantum discord, as well as its classical
counterpart, measurement-induced disturbance and the
Clauser-Horne-Shimony-Holt-Bell function. Measurement-induced disturbance is
found to detect the first and second order phase transitions present in these
critical systems, while, surprisingly, it is found to fail to signal the
infinite-order phase transition present in the XXZ model. Remarkably, the
Clauser-Horne-Shimony-Holt-Bell function is found to detect all the phase
transitions, even when quantum and classical correlations are zero for the
relevant ground state.
