Analytic theory of correlation energy and spin polarization in the 2D   electron gas
  We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schr\"odinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength $r_s\approx 24$ from the paramagnetic to the fully spin-polarized fluid. 
R. Asgari, B. Davoudi and M. P. Tosi