Spin polarization of the low-density three-dimensional electron gas

To determine the state of spin polarization of the three-dimensional electron gas at very low densities and zero temperature, we calculate the energy versus spin polarization using diffusion quantum Monte Carlo methods with backflow wave functions and twist averaged boundary conditions. We find a second-order phase transition to a partially polarized phase at $r_s\sim 50\pm 2.$ The magnetic transition temperature is estimated using an effective mean-field method, the Stoner model.