Spin polarization in a two-dimensional electron gas

We evaluate the charge and longitudinal spin response functions of a two-dimensional electron gas with $e^2/r$ interactions in an arbitrary state of spin polarization, using a structurally self-consistent approach to treat exchange and correlations. From the results we assess the nature of the magnetic order in the electronic ground state in zero magnetic field as a function of electron density. We find that states of partial spin polarization are thermodynamically unstable at all values of the coupling strength and that a first-order phase transition occurs with increasing coupling strength from the magnetically disorderd (paramagnetic) phase to the fully spin-polarized (ferromagnetic) phase. This behavior is in qualitative agreement with diffusion Monte Carlo data, although the location of the phase transition is underestimated in our calculations.