The Effective Spin Hamiltonian and Phase Separation Instability of the Almost Half-Filled Hubbard Model and Narrow-Band {\it S-f} Model

Abstract

The effective spin Hamiltonian is constructed in the framework of the almost half-filled Hubbard model on the Cayley tree by means of functional integral technique with the use of static approximation. The system in the ground state appears to be consisting of the ferromagnetic metallic domains and the antiferromagnetic insulating one sprovided that the concentration of excess electrons (or holes) does not exceed some critical value. The connection between the Hubbard model and the {\it s-f} model is stated. Note added: This posting is intended to show that the phase separation in strongly correlated electronic systems was considered already in 1970-80's and is not a discovery of latest manganites boom