Beyond universality in repulsive SU(N) Fermi gases

Itinerant ferromagnetism in dilute Fermi gases is predicted to be at values of the gas parameter where second-order perturbation theory is not accurate enough. We have revisited perturbation theory up to third order for SU(N) fermions and found its generalization in terms of both the gas parameter and spin polarization. At difference with recent derivations of the same type at second-order, we have not been able to end up with a fully analytical result. Instead, we worked out analytically some of the terms and integrated numerically the rest. Our results agree satisfactorily with quantum Monte Carlo results for $s=1/2$ and hard-sphere interactions. For any value of the spin, we observe a discontinuous ferromagnetic transition but for $s=1/2$ the gap in the polarization at the transition is very small resembling more a quasi-continuous transition.Comment: 13 pages, 32 figure