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 +/- 5 less than or equal to r(s) less than or equal to 40 +/- 5) for the partially spin-polarized liquid. The freezing transition into a ferromagnetic Wigner crystal occurs at r(s) = 65 +/- 10. We discuss the relative stability of different magnetic structures in the solid phase.
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