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arXiv · 2607.13675

Stoner transitions beyond mean-field in two-dimensional electronic systems: a diagrammatic Monte Carlo study

Yueh-Chen Lee·Nikolay V. Prokof'ev·Andrey V. Chubukov
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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.

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Yueh-Chen Lee, Nikolay V. Prokof'ev, Andrey V. Chubukov. 2026-07-15. Stoner transitions beyond mean-field in two-dimensional electronic systems: a diagrammatic Monte Carlo study. https://arxiv.org/abs/2607.13675

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