Spin Polarization of the Low Density 3D Electron Gas

To determine the state of spin polarization of the 3D electron gas at very low densities and zero temperature, we calculate the energy versus spin polarization using Diffusion Quantum Monte Carlo methods with backflow wavefunctions and twist averaged boundary conditions. We find a second order phase transition to a partially polarized phase at r_s = 50 \pm 2. The magnetic transition temperature is estimated using an effective mean field method, the Stoner model.