We consider the competition of magnetic and charge ordering in model cuprate 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 classicalMonte 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 pseudospin (charge) and magnetic (spin) subsystems, which behave like immiscible quantum liquids. An analytical expression was obtained for the PS temperature. The research was supported by the Government of the Russian Federation, Program 02.A03.21.0006 and by the Ministry of Education and Science of the Russian Federation, projects Nos. 2277 and 5719, and RFBR N 18-32-0083718.

We consider a two-dimentional spin-pseudospin model to study the critical properties of a diluted Ising magnet. The model with charged impurities is frustrated due to competition between charge and spin orders. We used classical Monte Carlo method to obtain the ground state phase diagram, and study unconventional phase states at finite temperatures, including order-order and reentrant phase transitions.