  We discuss spontaneously broken quantum field theories with a continuous
symmetry group via the constraint effective potential. Employing lattice
simulations with constrained values of the order parameter, we demonstrate
explicitly that the path integral is dominated by inhomogeneous field
configurations and that these are unambiguously related to the flatness of the
effective potential in the broken phase. We determine characteristic features
of these inhomogeneities, including their topology and the scaling of the
associated excess energy with their size. Concerning the latter we introduce
the differential surface tension -- the generalization of the concept of a
surface tension pertaining to discrete symmetries. Within our approach,
spontaneous symmetry breaking is captured merely via the existence of
inhomogeneities, i.e. without the inclusion of an explicit breaking parameter
and a careful double limiting procedure to define the order parameter. While
here we consider the three-dimensional $O(2)$ model, we also elaborate on
possible implications of our findings for the chiral limit of QCD.
