Magnetic properties of the three-dimensional Hubbard model at half filling

TL;DR

This paper investigates the magnetic properties of the three-dimensional Hubbard model at half-filling using the TPSC formalism, revealing good agreement with other methods and highlighting differences from 2D and anisotropic cases.

Contribution

It extends the TPSC approach to the 3D Hubbard model, providing detailed analysis of magnetic transitions and local correlations, and compares results with DMF and Monte Carlo methods.

Findings

Good quantitative agreement with DMF for isotropic 3D model

Finite size lattice calculations agree with Monte Carlo results in intermediate coupling

Qualitative difference in double occupation factor between isotropic 3D and 2D or anisotropic 3D cases

Abstract

We study the magnetic properties of the 3d Hubbard model at half-filling in the TPSC formalism, previously developed for the 2d model. We focus on the N\'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with Dynamical Mean-Field results for the isotropic 3d model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3d case, and the 2d or anisotropic 3d cases for the double occupation factor. Even for this local correlation function, 2d or anisotropic 3d cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.