Stoner ferromagnetism of a strongly interacting Fermi gas in the quasirepulsive regime

Recent advances in rapidly quenched ultracold atomic Fermi gases near a Feshbach resonance arise a number of interesting problems, in the context of observing the long-sought Stoner ferromagnetic phase transition. The possibility of experimentally obtaining a ``quasirepulsive'' regime in the upper branch of the energy spectrum due to the rapid quench is currently debated and theoretically, the Stoner transition has mainly been investigated at zero temperature or high polarization, due to the limited theoretical approaches in the strongly repulsive regime. Here, we develop a nonperturbative large-N expansion theory for a quasirepulsive Fermi gas near resonance and present a finite temperature phase diagram for its Stoner instability. Our results agree well with the known quantum Monte-Carlo simulations at zero temperature and recover the virial expansion prediction at high temperature for arbitrary interaction strengths. At resonance, we find that the unitary Fermi gas undergoes the Stoner transition at about 1.5TF, where TF is the Fermi degeneracy temperature.