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The competition of charge and spin orderings is a challenging problem for strongly correlated systems, in particular, for high-T c  cuprates. We addressed a simplified static 2D spin-pseudospin model which takes into account both conventional spin exchange coupling and the on-site and inter-site charge correlations. Classical Monte-Carlo calculations for large square lattices show that homogeneous ground state antiferromagnetic solutions found in a mean-field approximation are unstable with respect to phase separation into the charge and spin subsystems behaving like immiscible quantum liquids. In this case, with lowering of a temperature one can observe two sequential phase transitions: first, antiferromagnetic ordering in the spin subsystem diluted by randomly distributed charges, then, the charge condensation in the charge droplets. The inhomogeneous droplet phase reduces the energy of the system and changes the diagram of the ground states. On the other hand, the ground state energy of charge-ordered state in a mean-field approximation exactly matches the numerical Monte-Carlo calculations. The doped charges in this case are distributed randomly over a system in the whole temperature range. Various thermodynamic properties of the 2D spin-pseudospin system are studied by Monte-Carlo simulation.

Unconventional phase separation in the model 2D spin-pseudospin system