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The free energy of a nonabelian gauge theory at high temperature T can be calculated to order g^5 using resummed perturbation theory, but the method breaks down at order g^6. A new method is developed for calculating the free energy to arbitrarily high accuracy in the high temperature limit. It involves the construction of a sequence of two effective field theories by first integrating out the momentum scale T and then integrating out the momentum scale g T. The free energy decomposes into thedoi:10.1103/physrevlett.74.2164 pmid:10057859 fatcat:z2z5x57ntjbp7mxadgst5276dq