Self-consistent approach for thermodynamics of a simplified   pseudospin-electron model
  We present the method of the self-consistent calculation of thermodynamical and correlation functions. This approach is based on the GRPA (generalized random phase approximation) scheme with the inclusion of the mean field corrections.   Investigation of a pseudospin-electron model (PEM) within the framework of the presented method shows that interaction between the electron and pseudospin subsystems leads to the possibility of either first or second order phase transitions between different uniform phases (bistability) as well as between the uniform and the chess-board ones.   In the regime n=const, an instability with respect to phase separation in the electron and pseudospin subsystems can take place. 
I.V.Stasyuk, A.M.Shvaika and K.V.Tabunshchyk