The effective spin hamiltonian and phase separation instability of the almost half-filled hubbard model and the narrow-band s-ƒ model

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 s-f{hook} model is stated.