Symmetry breaking

(physics) The deviation from exact symmetry exhibited by many physical systems; it encompasses explicit symmetry breaking and spontaneous symmetry breaking.

A deviation from exact symmetry. According to modern physical theory the fundamental laws of physics possess a very high degree of symmetry. Several deep insights into nature arise in understanding why specific physical systems, or even the universe as a whole, exhibit less symmetry than the laws themselves.

Spontaneous symmetry breaking

This mechanism occurs in quite diverse circumstances. The most symmetrical solutions of the fundamental equations governing a given system may be unstable, so that in practice the system is found to be in a less symmetrical, but stable, state. When this occurs, the symmetry is said to have been broken spontaneously.

For example, the laws of physics are unchanged by any translation in space, but a crystalline lattice is unchanged only by special classes of translations. A crystal does retain a large amount of symmetry, for it is unchanged by those finite translations, but this falls far short of the full symmetry of the underlying laws. See also Crystal structure.

Another example is provided by ferromagnetic materials. The spins of electrons within such materials are preferentially aligned in some particular direction, the axis of the poles of the magnet. The laws of physics governing the interactions among these spins are unchanged by any rotation in space, but the aligned configuration of spins has less symmetry. Indeed, it is left unchanged only by rotations about the polar axis. See also Ferromagnetism.

In both these examples, the loss of symmetry is associated with the appearance of order. This is a general characteristic of spontaneous symmetry breaking.

Consequences

There is a cluster of important observable consequences associated with spontaneous symmetry breaking.

Nambu-Goldstone bosons are a class of low-energy excitations associated with gentle variations of the order. Thus, there is a class of excitations of the ferromagnet, the magnons, that exist as a consequence of the spontaneous symmetry breaking, and that have very low energy. Similarly, in the case of crystals, phonons are associated with gentle distortions of the lattice structure. See also Magnon; Phonon.

At high temperatures the energy gained by assuming an ordered structure is increasingly outweighed by the entropy loss associated with the constraints it imposes, and at some point it will no longer be favorable to have spontaneous symmetry breaking in thermal equilibrium. Changes from broken symmetry to unbroken symmetry are marked by phase transitions. For a magnet, the transition occurs at the Curie temperature. For a crystal, it is melting into a liquid or sublimation into a gas. See also Curie temperature; Entropy; Phase transitions.

Defects are imperfections in the ordering. The most familiar examples are domain walls in magnets. See also Crystal defects; Domain (electricity and magnetism).

In systems with long-range forces as well as spontaneous symmetry breaking, it need no longer be true that gradual changes require only a small input of energy, because even distant regions interact significantly. Thus, the Nambu-Goldstone bosons no longer have very low energies, and they are not easily excited. Conversely, the system will exhibit a special rigidity, with strong correlations between distant points. These ideas are central to modern theories of superconductivity and of particle physics (the Higgs mechanism). See also Electroweak interaction; Higgs boson; Superconductivity.