Spontaneous symmetry breaking is a mode of realization of symmetry breaking in a physical system, where the underlying laws are invariant under a symmetry transformation, but the system as a whole changes under such transformations, in contrast to explicit symmetry breaking. It is a spontaneous process by which a system in a symmetrical state ends up in an asymmetrical state. It thus describes systems where the equations of motion or the Lagrangian obey certain symmetries, but the lowest energy solutions do not exhibit that symmetry.
Consider the bottom of an empty wine bottle, a symmetrical upward dome with a gutter for sediment. If a ball is placed at the peak of the dome, the situation is symmetrical with respect to rotating the wine bottle. But the ball may spontaneously break this symmetry and roll into the gutter, a point of lowest energy. The bottle and the ball retain their symmetry, but the system does not.
Most simple phases of matter and phase-transitions, like crystals, magnets, and conventional superconductors can be simply understood from the viewpoint of spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the fractional quantum Hall effect.
Read more about Spontaneous Symmetry Breaking: Generalisation and Technical Usage, A Pedagogical Example: The Mexican Hat Potential, Other Examples, Nobel Prize
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