# symmetry breaking

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## 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 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 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 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 Curie temperature, Entropy, Phase transitions, Thermodynamic principles

Defects are imperfections in the ordering. The most familiar examples are domain walls in magnets. See 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 Electroweak interaction, Higgs boson, Superconductivity

## symmetry breaking

[′sim·ə·trē ‚brāk·iŋ]
(physics)
The deviation from exact symmetry exhibited by many physical systems; it encompasses explicit symmetry breaking and spontaneous symmetry breaking.
References in periodicals archive ?
Kelley, "Chiral symmetry breaking in the soft-wall AdS/QCD model," Physical Review D, vol.
And he mentioned terahertz-speed symmetry breaking.
Chiral symmetry breaking and the origins of homochirality of organic molecules Kenso SOAI Communicated by Kenji MORI, M.J.A.
Reaching energies of 100 TeV and beyond would allow precise studies of how a Higgs particle interacts with another Higgs particle, and thorough exploration of the role of the electroweak symmetry breaking in the history of our universe.
Niu, "Valley-dependent optoelectronics from inversion symmetry breaking," Physical Review B: Condensed Matter and Materials Physics, vol.
In QG research, it is known that general relativity with nonzero cosmological constant ([LAMBDA] [not equal to] 0) can be obtained from a so-called BF model (a topological field theory) for a gauge field, valued in either SO(3,2) (for [LAMBDA] < 0) or a SO(4,1) (for [LAMBDA] > 0), by a symmetry breaking mechanism [6,7].
Left-right (LR) symmetry breaking events are an important aspect of embryogenesis.
"The Higgs boson plays a crucial role in our world - it provides mass to the Z and to the related W particles through a mechanism known as electroweak symmetry breaking.
In the ensuing decades, though, further refinements have made it the go-to technique for calculating excited states, including in open-shell atoms, as well as for many other properties such as phase transitions, spontaneous symmetry breaking and topological excitation.
observed Fano resonance in a planar metallic metamaterial structure by introducing symmetry breaking [15].

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