Magnetic Phase Diagram of Hubbard Model in Three Dimensions: the Second-Order Local Approximation

TL;DR

This paper applies a second-order local approximation to the 3D Hubbard model, revealing temperature-dependent magnetic phase transitions including antiferromagnetism and incommensurate SDW states, consistent with experimental observations.

Contribution

It introduces a second-order local approximation to analyze the magnetic phase diagram of the 3D Hubbard model, capturing both commensurate and incommensurate SDW states.

Findings

Paramagnetic state becomes unstable towards SDW at lower temperatures.

Incommensurate SDW wavevector remains close to the commensurate one.

Results align with experimental data for chromium alloys.

Abstract

A local, second-order (truncated) approximation is applied to the Hubbard model in three dimensions. Lowering the temperature, at half-filling, the paramagnetic ground state becomes unstable towards the formation of a commensurate spin-density-wave (SDW) state (antiferromagnetism) and sufficiently far away from half-filling towards the formation of incommensurate SDW states. The incommensurate-ordering wavevector does not deviate much from the commensurate one, which is in accord with the experimental data for the SDW in chromium alloys.