Pseudospin-Electron Model in Large Dimensions
  Energy spectrum and thermodynamics of the pseudospin-electron model introduced at the consideration of the anharmonicity effects in high-$T_c$ superconductors are investigated in the dynamical mean field approximation ($d=\infty$ limit). In the limit of zero electron correlation $U\to 0$ this model is analytically exactly soluble within this approach: in the $\mu=const$ regime the first order phase transition with the jump of the pseudospin mean value $<S^z>$ and reconstruction of the electron spectrum can realize, while in the $n=const$ regime the phase separation in electron subsystem can take place for certain values of the model parameters. On the basis of the obtained results the applicability of the approximate schemes previously used for the investigation of the pseudospin-electron model are discussed. 
I.V. Stasyuk and A.M. Shvaika