Examples for SSB

• Consider a needle standing vertically on its end. The system has a continuous azimuthal symmetry, i.e., it is rotationally symmetric around the vertical axis. The angle of rotation can take any value between 0 and 2π. The ground state corresponds to the needle having fallen. It can fall in any direction, however, the ground state does not share the azimuthal symmetry of the system.
• Consider a circular table with four equally spaced chairs. The system has a discrete rotational symmetry, i.e., it is rotationally symmetric around the vertical axis, but only for rotations of 0, π/2, π, and 3π/2. The ground state corresponds to the first guest taking a seat. The guest can take any seat, however, rotating by π/2 does not leave the ground state invariant: the guest is now sitting in a different seat.
• Consider a ferromagnet. Above the critical temperature, the individual (microscopic) magnetic dipoles are randomly aligned, leading to an average (macroscopic) magnetization of zero. The system has a continuous rotational symmetry. However, below the critical temperature of the dipoles align, yielding to a non-zero average (macroscopic) magnetization. This ground state does not share the original continuous rotational symmetry of the system, since the macroscopic magnetic field points in a specific direction. However, we can still rotate the magnet around the axis of its magnetic field, leaving intact a (lesser) continuous rotational symmetry.