  We explore the Coleman-Weinberg phase transition in regions outside the
validity of perturbation theory. For this purpose we study a Euclidean field
theory with two scalars and discrete symmetry in four dimensions. The phase
diagram is established by a numerical solution of a suitable truncation of
exact non-perturbative flow equations. We find regions in parameter space where
the phase transition (in dependence on the mass term) is of the second or the
first order, separated by a triple point. Our quantitative results for the
first order phase transition compare well to the standard perturbative
Coleman-Weinberg calculation of the effective potential.
