  We have used quantum Monte Carlo methods to calculate the zero-temperature
phase diagram of the two-dimensional homogeneous electron gas. We find a
transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner
crystal at density parameter r_s=31(1) a.u. and a transition to a ferromagnetic
crystal at r_s=38(5) a.u. The fully spin-polarized fluid is never stable. We
searched for, but did not find, the ferromagnetic hybrid phase proposed by H.
Falakshahi and X. Waintal [Phys. Rev. Lett. 94, 046801 (2005)].
