Spontaneous Symmetry Breaking

has a local maximum rather than a minimum at phase-symmetric point Φ = 0. Instead, it has a continuous ring of degenerate minima at Φ = v × any phase. None of these minima is invariant under the U(1) phase symmetry; instead, the symmetry relates the minima to each other. Semiclassically — and hence in perturbation theory, or even non-perturbatively for small enough λ, — this means that the theory does not have a unique physical vacuum but rather a continuous family of exactly degenerate vacua related to each other by the phase symmetry. This phenomenon is called spontaneous breakdown of the symmetry.