  We study the deconfining phase transition in 3+1 dimensional pure SU(N)
Yang-Mills theory using a gauge invariant variational calculation. We
generalize the variational ansatz of Phys. Rev. D52, 3719 (1995) to mixed
states (density matrices) and minimize the free energy. For N > 3 we find a
first order phase transition with the transition temperature of T_C = 450 Mev.
Below the critical temperature the Polyakov loop has vanishing expectation
value, while above T_C, its average value is nonzero. According to the standard
lore this corresponds to the deconfining transition. Within the accuracy of our
approximation the entropy of the system in the low temperature phase vanishes.
The latent heat is not small but, rather, is of the order of the
nonperturbative vacuum energy.
