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

TL;DR

This paper constructs an effective spin Hamiltonian for the nearly half-filled Hubbard model on a Cayley tree, revealing phase separation into ferromagnetic and antiferromagnetic domains, and discusses historical context of phase separation in correlated systems.

Contribution

It introduces a static approximation-based effective spin Hamiltonian for the Hubbard model and links it to the s-f model, highlighting phase separation phenomena.

Findings

Ground state consists of ferromagnetic metallic and antiferromagnetic insulating domains.

Phase separation occurs when excess electron or hole concentration is below a critical value.

Historical context shows phase separation was studied in the 1970s-80s, not a recent discovery.

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