Spontaneous symmetry breaking

Spontaneous symmetry breaking occurs when a system’s governing laws have a symmetry but its realized state does not, without an external influence explicitly breaking that symmetry.

Symmetry: A transformation that leaves an object, system, or law unchanged. The governing laws retain symmetries that the selected state lacks.
Ferromagnetism: The tendency of a material’s magnetic moments to align, producing spontaneous magnetization. A magnet’s chosen direction breaks rotational symmetry in the absence of an aligning field.
Explicit symmetry breaking: Symmetry breaking caused by terms or influences that make the governing laws themselves asymmetric. Unlike spontaneous breaking, the asymmetry is already present in the laws or external conditions.
Pierre Curie: A French physicist who studied symmetry principles in physical phenomena and crystal formation. His symmetry principles helped establish how physical causes constrain possible effects.
Phase transition: A change between distinct states of matter marked by a qualitative change in physical properties. Spontaneous symmetry breaking often characterizes ordered phases appearing at a transition.
Order parameter: A quantity that distinguishes phases or states by capturing their macroscopic order. Its nonzero value often signals that the realized state is asymmetric.
Ising model: A model of interacting spins that take one of two values on a lattice. Below its critical temperature, it provides a canonical discrete-symmetry-breaking transition.
Continuous symmetry: A symmetry whose transformations vary continuously, such as rotations through arbitrary angles. Breaking a continuous symmetry can produce Goldstone modes.
Lev Landau: A Soviet physicist who developed a theory of phase transitions using order parameters. His framework made symmetry-breaking phases describable through changing order parameters.
Critical phenomena: Universal behavior of systems near continuous phase transitions, including scaling and long-range correlations. Near a symmetry-breaking transition, fluctuations can dominate and produce universal behavior.

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