On the Ordering Instability of Weakly-Interacting Electrons in a Dirty Metal

TL;DR

This paper demonstrates that electron-electron interactions in dirty metals can induce ferromagnetism, with a detailed calculation showing the emergence of a finite magnetic moment as the system's stable state.

Contribution

It provides a theoretical analysis of how singular corrections due to interactions lead to ferromagnetic order in disordered metals, using an effective action approach.

Findings

Singular corrections signal ferromagnetic instability.

Finite ferromagnetic moment minimizes the effective action.

Large-N limit makes the saddle-point approximation exact.

Abstract

In a dirty metal, electron-electron interactions in the spin-triplet channel lead to singular corrections to a variety of physical quantities. We show that these singularities herald the emergence of ferromagnetism. We calculate the effective action for the magnetic moment of weakly-interacting electrons in a dirty metal and show that a state with finite ferromagnetic moment minimizes this effective action. The saddle-point approximation is exact in an appropriate large-N limit. We discuss the physics of the ferromagnetic state with particular regard to thermal fluctuations and localization effects.