  We study the nature of the confinement phase transition in d=3+1 dimensions
in various non-abelian gauge theories with the approach put forward in [1]. We
compute an order-parameter potential associated with the Polyakov loop from the
knowledge of full 2-point correlation functions. For SU(N) with N=3,...,12 and
Sp(2) we find a first-order phase transition in agreement with general
expectations. Moreover our study suggests that the phase transition in E(7)
Yang-Mills theory also is of first order. We find that it is weaker than for
SU(N). We show that this can be understood in terms of the eigenvalue
distribution of the order parameter potential close to the phase transition.
