Thermodynamics of pseudospin-electron model in mean field approximation
  The mean field type approach based on the self-consistent consideration of an effective field created by electron transfer is developed for a description of thermodynamics of the Hubbard type models with an infinitely large on-site repulsion. This procedure, formulated by Izyumov et al, is an extension of the recently proposed generalized random phase approximation(GRPA).   Within this approach, the thermodynamic properties of the two-sublattice pseudospin-electron model (the Hubbard model with local anharmonicity) are studied. Such a model can be used for a description of dielectric properties of YBaCuO-type superconductors along c-axis; pseudospins represent anharmonic motions of apical oxygens O4. It is shown that there are either phase transitions in the model with jumps of the mean values of a pseudospin and of electron concentration (in the $\mu=const$ regime) or the phase separation (in the $n=const$ regime). The phase transitions or phase separation are caused by pseudospin-pseudospin interaction as well as by electron transfer (the latter results in appearing of effective interaction between pseudospins). The possibility of the ferroelectric type ordering of pseudospins is investigated. 
I.V.Stasyuk, O.D.Danyliv