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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.
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.
Those lines are high-symmetry residuals within the symmetry broken phase. It is characteristic for a continuous phase transition that the energy difference between ordered and disordered phase disappears at the transition point. This implies that fluctuations between both phases will become arbitrarily large.
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.
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 ...
Charge ordering (CO) is a (first- or second-order) phase transition occurring mostly in strongly correlated materials such as transition metal oxides or organic conductors. Due to the strong interaction between electrons, charges are localized on different sites leading to a disproportionation and an ordered superlattice .