Global quantum discord in an Ising model with transverse and longitudinal magnetic fields

Global quantum discord (GQD) refers to the number of quantum correlations present in the entire quantum many-body system, rather than just between two subsystems. Here, we utilize GQD to characterize quantum phase transitions in an Ising chain subjected to both transverse and longitudinal magnetic fields. We investigate the effects of the transverse magnetic field \(h_{x}\), longitudinal magnetic field \(h_{z}\), and temperature T on the properties of GQD while keeping the coupling strength J between spins constant. We show that we can perfectly illustrate the critical points of the model by analyzing the singularity of GQD. We find that the GQD exhibits an increase as the system size N increases, regardless of whether the temperature is zero or finite. We present the phase diagram of a mixed Ising model under the combined influence of \(h_{x}\) and \(h_{z}\). Moreover, we show that we can use the features of GQD at lower temperatures to identify QPTs in quantum many-body systems and determine their critical points, as achieving absolute zero temperatures is practically impossible. Additionally, we show that GQD both at zero and finite temperatures show a linear behavior of the system size N, i.e., \(\mathcal {G}=kN+b\), in which k and b are the fitting parameters.