Phase transitions of repulsive two-component fermi gases in two dimensions

We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory systematic semiclassical approximations, we address long-standing problem itinerant ferromagnetism in realistic settings. reveal a universal transition from paramagnetic state at small towards ferromagnetic density profiles large interaction strengths, intricate particle-number dependent phases between. Building on quantum Monte Carlo results for uniform systems, benchmark our simulations against Hartree-Fock calculations number trapped fermions. thereby demonstrate that employed corrections to mean-field energy and especially Thomas-Fermi kinetic are necessary reliably predicting properties mesoscopic gases. The patterns ground survive low finite temperatures confirm Stoner-type polarization behavior across parameter, albeit substantial quantitative differences originate trapping potential quantum-corrected energy. also uncover zoo metastable configurations energetically comparable ground-state thus likely be observed experiments. argue density-functional approach can easily applied interacting multi-component general.