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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.
Spontaneous symmetry breaking is a phenomenon that occurs in various fields of physics, particularly in condensed matter physics, particle physics, and cosmology. It describes a situation in which a system that is symmetric under some transformation settles into an asymmetrical state. Despite the underlying laws or equations being symmetric, the actual observed state of the system does not exhibit this symmetry.