This phenomenon is the basis of Landau's theory of second-order phase transitions.
In two spacetime dimensions, this effect never truly happens, being prohibited by strong quantum fluctuations as shown by Coleman, Mermin, and Wagner. Antiferromagnets exhibit this phenomenon for both time reversal and translations. Magnetization of the Ising model below a critical temperature is another example, as is superfluidity. Elitzur showed that for gauge theories it does not happen, although the Higgs mechanism provides a close analogue. This phenomenon is the basis of Landau's theory of second-order phase transitions. It leads to a gapless excitation, or Nambu-Goldstone boson. For 10 points, what is this phenomenon in which microscopic physics is invariant under a given symmetry but the ground state is not?
In two spacetime dimensions, this effect never truly happens, being prohibited by strong quantum fluctuations as shown by Coleman, Mermin, and Wagner.
spontaneous symmetry breaking [prompt on "symmetry breaking"]