Mechanisms of finite temperature magnetism in the three-dimensional Hubbard model

TL;DR

This paper investigates the transition to antiferromagnetic order in the 3D Hubbard model at finite temperature using the dual-fermion approach, revealing different regimes dominated by spin-flip excitations and Heisenberg physics.

Contribution

It provides a detailed analysis of the magnetic transition across weak, intermediate, and strong coupling regimes in the 3D Hubbard model using a multiscale dual-fermion method.

Findings

Spin-flip excitations are crucial in the weak-coupling regime.

Strong coupling behavior aligns with Heisenberg physics.

Critical exponents match Heisenberg universality class down to U/t=10.

Abstract

We examine the nature of the transition to the antiferromagnetically ordered state in the half-filled three-dimensional Hubbard model using the dual-fermion multiscale approach. Consistent with analytics, in the weak-coupling regime we find that spin-flip excitations across the Fermi surface are important, and that the strong coupling regime is described by Heisenberg physics. In the intermediate interaction, strong correlation regime we find aspects of both local and non-local correlations. We analyze the critical exponents of the transition in the strong coupling regime and find them to be consistent with Heisenberg physics down to an interaction of $U/t=10$.