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 profil...

let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...