# A Replica Stoner Theory for Dirty Ferromagnets

## TL;DR

This paper develops a theoretical framework combining replica and Stoner mean-field theories to analyze how disorder influences ferromagnetism, revealing disorder-enhanced ferromagnetism and the potential emergence of spin-glass phases.

## Contribution

It introduces a novel combined replica-Stoner mean-field approach to study disorder effects on ferromagnetic metals, including phase diagram construction and disorder-induced ferromagnetism.

## Key findings

- Disorder can enhance ferromagnetism in dirty ferromagnets.
- A spin-glass phase may appear at high disorder levels.
- Disorder can induce ferromagnetism in systems non-ferromagnetic in the clean limit.

## Abstract

This paper investigates the effect of disorder on a ferromagnetic metal with repulsive interactions. We assume that, in the clean limit, the ferromagnetic state can be described by Stoner mean-field theory and study how disorder affects the the system by using a combined replica + Stoner mean-field approach. At zero temperature, we find that a replica-symmetric ferromagnetic mean-field solution exists in the presence of disorder with a modified Stoner criteria where the ferromagnetism is enhanced by disorder. At finite temperature, a Landau theory is employed to construct the phase diagram, revealing that beyond a critical disorder strength, a spin-glass phase may exist between the high-temperature paramagnetic phase and the low-temperature ferromagnetic phase. For weak (repulsive) interaction where the system is non-ferromagnetic in the clean limit, the possibility of a disordered-induced ferromagnetic ground state is observed both at zero temperature and finite temperature. The potential applicability of this framework to realistic materials is briefly discussed.