The Three-Loop Free Energy for High-Temperature QED and QCD with   Fermions
  We compute the free energy density for gauge theories, with fermions, at high temperature and zero chemical potential. Specifically, we analytically compute the free energy through $O(g^4)$, which requires the evaluation of three-loop diagrams. This computation extends our previous result for pure gauge QCD. 
Peter Arnold and Chengxing Zhai