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Spontaneous symmetry breaking occurs when the action and equations have a symmetry but a chosen ground state is invariant only under a proper subgroup. Acting with the broken symmetry generates a degenerate vacuum manifold. An order parameter distinguishes the selected states: the equations do not prefer its direction, yet a particular state does. This lets one use the symmetry of the laws to predict excitations around a state that has less symmetry, notably the Goldstone bosons of a broken continuous symmetry.

A finite system with symmetry-preserving boundary conditions can have a symmetric ground state; a symmetric statistical mixture of broken states also has vanishing mean order parameter. A nonzero mean therefore requires a stated selection procedure. The symmetry-breaking order of limits takes the thermodynamic limit in a small applied source before removing that source. The finite-volume angular source selection example makes the distinction explicit for a continuous symmetry.