Stoner transitions beyond mean-field in two-dimensional electronic systems: a diagrammatic Monte Carlo study
arXiv:2607.13675
The paper investigates ferromagnetic Stoner transitions in two‑dimensional electron systems with one or two valleys beyond the mean‑field ladder approximation, using diagrammatic Monte Carlo to treat both ladder and non‑ladder renormalizations and identifying how momentum cutoffs and dispersion anisotropy affect the transition pathways.
Abstract
Stoner instabilities for fermions with repulsive interaction have been well studied within the mean-field (ladder) approximation. In this study, we consider two-dimensional electronic systems with one or two valleys and discuss a Stoner transition beyond the ladder approximation. At weak coupling, the corrections to the ladder approximation come predominantly from the renormalization of the particle-hole vertex in the particle-particle channel, and the lowest-order corrections are logarithmically singular in the low-density limit. To investigate the problem beyond the lowest order, we apply the diagrammatic Monte Carlo algorithm and treat ladder and non-ladder renormalizations on equal footing. We find that in a one-valley system, a Stoner transition to a ferromagnetism occurs at low density only if there is a cutoff on the momentum transfer carried by the interaction. In a two-valley system, the restriction is less severe. Here we find either a direct Stoner transition into a spin- and valley-polarized state, or a set of two Stoner transitions via an intermediate valley-polarized state. The pathway is controlled by the anisotropy of the fermionic dispersion.
35 pages, 17 figures