We investigate the role of inhomogeneous field configurations in systems with a spontaneously broken continuous global symmetry. Spontaneous breaking is usually defined as a specific double limit, first infinite volume at finite explicit breaking sources, which are then extrapolated to zero. We consider a different approach in which the order parameter is constrained under the path integral, which we simulate using lattice Monte Carlo techniques. In this way we access the flat region of the effective potential and we show that inhomogeneous configurations are dominant there. We topologically classify the important configurations and measure the excess energy stored in the inhomogeneities allowing for the definition of a generalized differential surface tension. We show that this contribution becomes negligible at large volumes restoring the flatness of the effective potential in the thermodynamic limit.