Two-dimensional Stoner transitions beyond mean field

We have previously shown that the Stoner instability two-dimensional has unconventional behavior: it is strongly first order but features a susceptibility which diverges at the transition point. Here, we analyze the Stoner transition for two-dimensional systems with spin and valley degrees of freedom, beyond mean field. At low density, we show that in one-valley and isotropic two-valley systems the leading effect beyond mean-field theory is suppression of the Stoner instability. In anisotropic two-valley systems, we show that, for larger anisotropy, the transition remains mean-field-like and retains its unconventional properties. We discuss applications to AlAs quantum wells.