Interaction effects on the itinerant ferromagnetism phase transition

TL;DR

This paper extends the analysis of itinerant ferromagnetism phase transitions in dilute Fermi liquids to third-order, revealing how additional interaction parameters influence the transition point and its nature across different spin values.

Contribution

It introduces third-order corrections involving effective range and p-wave scattering, showing their impact on the ferromagnetic phase transition and phase diagram.

Findings

Transition point shifts with new parameters

Nature of phase transition can change dramatically

Classification depends on interaction parameters, not just spin value

Abstract

Itinerant ferromagnetism is one of the most studied quantum phase transitions, the transition point and the nature of this phase transition being widely discussed. In dilute Fermi liquids, this analysis has been carried out up to second-order in the gas parameter, where the results for any spin degeneracy are universal in terms of only the s-wave scattering length $a_0$. We extend this analysis to third-order where energies depend, not only on $a_0$, but also on the s-wave effective range $r_0$ and the p-wave scattering length $a_1$. The introduction in the theory of these new parameters changes the transition point, with respect to the second-order estimation, and also can modify the nature of the phase transition itself. We analyze these interaction effects on the phase transition for different spin values. The emerging phase diagram shows that the type of ferromagnetic transition changes dramatically as a function of $r_0$ and $a_1$ and, importantly, that this classification is not solely determined by the spin value, as happens at second order.