Phase diagrams of a 2D Ising spin-pseudospin model

•The competition of spin and charge orderings in cuprates is examined.•The findings of the spin-pseudospin model are compared with the dilute Ising models.•The mean-field results are compared with the Monte Carlo calculations.•The found analytically phase separation temperature agrees with Monte Carlo results. We consider the competition of magnetic and charge ordering in high-Tc cuprates within the framework of the simplified static 2D spin-pseudospin model. This model is equivalent to the 2D dilute antiferromagnetic (AFM) Ising model with charged impurities. We present the mean-field results for the system under study and make a brief comparison with classical Monte Carlo (MC) calculations. Numerical simulations show that the cases of strong exchange and strong charge correlation differ qualitatively. For a strong exchange, the AFM phase is unstable with respect to the phase separation (PS) into the charge and spin subsystems, which behave like immiscible quantum liquids. An analytical expression was obtained for the PS temperature.