# Static spin susceptibility in magnetically ordered states

## TL;DR

This paper highlights the importance of correctly computing static spin susceptibility in magnetically ordered states, revealing that standard methods can lead to unphysical results if not properly adjusted, especially in metallic systems.

## Contribution

It demonstrates the necessity of including the derivative of the chemical potential in susceptibility calculations within magnetically ordered phases, using the 2D Hubbard model as a case study.

## Key findings

- The derivative of chemical potential w.r.t. magnetic field does not vanish in ordered phases.
- Magnetic susceptibility differs when computed at fixed density versus fixed chemical potential.
- Incorrect susceptibility calculations can lead to unphysical results in magnetically ordered metals.

## Abstract

We report that special care is needed when longitudinal magnetic susceptibility is computed in a magnetically ordered phase, especially in metals. We demonstrate this by studying static susceptibility in both a ferromagnetic and an antiferromagnetic state in the random phase approximation to the two-dimensional Hubbard model on a square lattice. In contrast to the case in the disordered phase, a first derivative of the chemical potential (or the density) with respect to a magnetic field does not vanish in a magnetically ordered phase when the field is applied parallel to the magnetic moment. This effect is crucial and should be included when computing magnetic susceptibility in the ordered phase, otherwise an unphysical result would be obtained. In addition, consequently the magnetic susceptibility becomes different when computed at a fixed density and a fixed chemical potential in the ordered phase. In particular, we cannot employ magnetic susceptibility at a fixed chemical potential to describe a system with a fixed density even if the chemical potential is tuned to reproduce the correct density.