On the validity of the static approximation in the spin-fluctuation theory for itinerant electrons

Abstract

The static approximation in the functional integral theory of itinerant magnetism is critically investigated. For the two-site Hubbard model the local magnetic moment and the specific heat are calculated as functions of temperature and interaction strength. By comparison with the exact results the error in the static approximation is found to be large at low temperatures and for small interaction strengths. It is shown that the subdivision of the ground state into a phase without a local moment (small interaction) and a phase with local moment (large interaction) is induced by the static approximation. The specific heat is underestimated and the zero-point entropy is finite. The implications for the infinite Hubbard model are briefly discussed.