Zero Temperature Phases of the Electron Gas

The stability of different phases of the three-dimensional nonrelativistic electron gas is analyzed using stochastic methods. With decreasing density, we observe a continuous transition from the paramagnetic to the ferromagnetic fluid, with an intermediate stability range ( $20\pm 5\le r_s\le 40\pm 5$) for the partially spin-polarized liquid. The freezing transition into a ferromagnetic Wigner crystal occurs at $r_s=65\mathrm{}\pm 10$. We discuss the relative stability of different magnetic structures in the solid phase.