Broken symmetry

Broken symmetry is a concept, developed by Lee and Yang, used in mathematics and physics when an object breaks either rotational symmetry or translational symmetry. That is, when one can only rotate an object in certain angles or when one is able to tell if the object has been shifted sideways (unless one shifts by a whole number of lattice units). For example, imagine a jumping bean sitting atop a  Mexican hat like the one pictured here. It is in a rotationally symmetric state until it inevitably hops and falls down to a lower equilibrium, breaking the rotational symmetry.
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