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Spontaneous symmetry breaking is also associated with phase transitions. For example in the Ising model , as the temperature of the system falls below the critical temperature the Z 2 {\displaystyle \mathbb {Z} _{2}} symmetry of the vacuum is broken, giving a phase transition of the system.
Consider a system that breaks some symmetry below a phase transition, which is characterized by an order parameter . This order parameter is a measure of the order before and after a phase transition; the order parameter is often zero above some critical temperature and non-zero below the critical temperature.
Spontaneous symmetry breaking illustrated: At high energy levels (left), the ball settles in the center, and the result is symmetric.At lower energy levels (right), the overall "rules" remain symmetric, but the symmetric "sombrero" enforces an asymmetric outcome, since eventually the ball must rest at some random spot on the bottom, "spontaneously", and not all others.
Symmetry-breaking phase transitions play an important role in cosmology. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the electroweak field into the U(1) symmetry of the present-day electromagnetic field.
The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science.
The superfluid is characterized by long-range phase coherence, a spontaneous breaking of the Hamiltonian's continuous () symmetry, a non-zero compressibility and superfluid susceptibility. At non-zero temperature, in certain parameter regimes a regular fluid phase appears that does not break the U ( 1 ) {\displaystyle U(1)} symmetry and does ...
The potential results in having the vacuum expectation value of = / at the electroweak phase transition. Spontaneous symmetry breaking of the Peccei–Quinn symmetry below the electroweak scale gives rise to a pseudo-Goldstone boson known as the axion a {\displaystyle a} , with the resulting Lagrangian taking the form [ 5 ]
Baryogenesis within the Standard Model requires the electroweak symmetry breaking to be a first-order cosmological phase transition, since otherwise sphalerons wipe off any baryon asymmetry that happened up to the phase transition. Beyond this, the remaining amount of baryon non-conserving interactions is negligible.