Exact energy of the spin-polarized two-dimensional electron gas at high   density
  We derive the exact expansion, to $O(r_s)$, of the energy of the high-density spin-polarized two-dimensional uniform electron gas, where $r_s$ is the Seitz radius. 
Pierre-Fran\c{c}ois Loos and Peter M. W. Gill
cond-mat.str-el cond-mat.other physics.chem-ph