Phase Diagrams of a 2D Dilute Antiferromagnetic Ising Model with Charged Impurities

In this work, we address a topical problem of a competition of charge and spin ordering for high-T cuprates. We have studied a simplified static 2D spin-pseudospin model on a square lattice, which takes into account both conventional antiferromagnetic spin exchange coupling and the on-site and intersite charge correlations in the CuO₂ planes with the on-site Hilbert space reduced to only three effective valent states. We compared an analytical results for the ground state and for the temperature phase diagrams obtained in a mean field approximation and a large amount of the classical Monte Carlo calculations. Numerical results show that homogeneous ground state antiferromagnetic solutions found in a mean field approximation are unstable for the "strong" exchange limit with respect to phase separation with the charge and spin subsystems behaving like immiscible quantum liquids. We found an analytical expression for critical temperature of phase separation and performed the comparison with the Monte Carlo results.