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* [[Ferromágnes]]es anyagok esetén az őket leíró törvények invariánsak a térbeli forgatásokkal szemben. Itt a rendparaméter a [[mágnesezettség]], ami a [[mágneses dipólus]]sűrűséget méri. A [[Curie-hőmérséklet]] felett a rendparaméter nulla, ami forgásinvariáns és nincs szimmetriasértés. A Curie-hőmérséklet alatt azonban a mágnesezettség állandó (az ideális helyzetben, teljes egyensúlyban, különben a transzlációs szimmetria is sérül) nemnulla értéket vesz fel, ami egy bizonyos irányba mutat. A maradék forgásszimmetriák, amik nem változtatják meg ezt az irányt, nem sérülnek, de a többi sérül.
* Egy szilárdtest invariáns a teljes [[Euklidészi csoport]]tal szemben, de a szilárdtest maga spontán sérti ezt a csoportot egy [[tércsoport]]ra. Az eltolás (elmozdulás) és az irány a rendparaméterek.
* A fizika törvényei invariánsak a térbeli forgatásokkal és eltolásokkal szemben, itt a Föld felszínén azonban van egy háttér gravitációs mező (ami a rendparaméter szerepét játsza), ami lefelé mutat, sértve a [[forgásszimmetria|forgásszimmetriát]]. Ez megmagyarázza a "fel", "le" és "vízszintes" irány miért "különböző", de a vízszintes irányok [[izotróp]]ok maradnak.
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*General relativity has a [[Lorentz gauge symmetry]], but in FRW cosmological models, the mean 4-velocity field defined by averaging over the velocities of the galaxies (the galaxies act like gas particles at cosmological scales) acts as an order parameter breaking this [[Lorentz symmetry]]. Similar comments can be made about the cosmic microwave background.
*Here on Earth, [[Galilean invariance]] (in the nonrelativistic approximation) is broken by the velocity field of the Earth/atmosphere, which acts as the order parameter here. This explains why people thought moving bodies tend towards rest before Galileo. We tend not to be aware of broken symmetries.
*For the electroweak model, as explained earlier, the Higgs field acts as the order parameter breaking the electroweak gauge symmetry to the electromagnetic gauge symmetry. Like the ferromagnetic example, there is a phase transition at the electroweak temperature. The same comment about us not tending to notice broken symmetries explains why it took so long for us to discover electroweak unification.
*For superconductors, there is a collective condensed matter field ψ which acts as the order parameter breaking the electromagnetic gauge symmetry.
*In [[general relativity]], [[diffeomorphism covariance]] is broken by the nonzero order parameter, the [[metric tensor]] field.
*Take a flat plastic [[ruler]] which is identical on both sides and push both ends together. Before buckling, the system is symmetric under the [[Reflection (mathematics)|reflection]] about the plane of the ruler. But after buckling, it either buckles upwards or downwards.
*Consider a uniform layer of [[fluid]] over an infinite horizontal plane. This system has all the symmetries of the Euclidean plane. But now heat the bottom surface uniformly so that it becomes much hotter than the upper surface. When the temperature gradient becomes large enough, [[convection cell]]s will form, breaking the Euclidean symmetry.
*Consider a bead on a circular hoop that is rotated about a [[diameter]]. As the [[rotational velocity]] is increased gradually from rest, the bead will initially stay at its initial [[equilibrium point]] at the bottom of the hoop (intuitively stable, lowest [[gravitational potential]]). At a certain critical rotational velocity, this point will become unstable and the bead will jump to one of two other newly created equilibria, [[equidistant]] from the center. Initially, the system is symmetric with respect to the diameter, yet after passing the critical velocity, the bead must choose between the two new equilibrium points, thus breaking symmetry. Note: This can easily be tried at home with an electric drill, a marble, and a pot cover, (or any other combination you can think of) and is the two-dimensional, mechanical analogue of the symmetry breaking that occurs in the [[Higgs Boson]] field
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==Külső hivatkozások==
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