Order parameter

An order parameter is a quantity that distinguishes phases by describing the degree and kind of order present, often through whether a symmetry is broken.

Spontaneous symmetry breaking: A system adopts a state with less symmetry than its governing laws or interactions. A nonzero order parameter often signals that the ordered phase has broken a symmetry.
Thermodynamic phase: A state of matter with uniform macroscopic properties and a distinct thermodynamic description. An order parameter distinguishes the phases on either side of an ordering transition.
Ferromagnetism: A form of magnetism in which aligned magnetic moments produce spontaneous magnetization. Magnetization serves as its standard order parameter.
Topological order: A kind of quantum order characterized by global properties and robust patterns of entanglement rather than local symmetry breaking. It can distinguish phases that share the same conventional local order parameter.
Landau theory: A framework that describes phase transitions using free energy expanded in powers of an order parameter. It predicts equilibrium phases by minimizing a free-energy function of the order parameter.
Symmetry (physics): A transformation that leaves the laws or physical properties of a system unchanged. The symmetry preserved or broken by a phase determines which order parameter can describe it.
Superconductivity: A state of matter with zero electrical resistance and expulsion of magnetic fields below a transition temperature. A complex-valued order parameter describes its macroscopic quantum state.
Crossover (physics): A smooth change in physical behavior without a thermodynamic phase transition. A smoothly varying quantity need not mark a sharp change of phase.
Critical exponent: A number that characterizes how a physical quantity varies near a continuous phase transition. The order parameter typically vanishes near a continuous transition with a characteristic critical exponent.
Phase transition: A change between distinct states of matter as conditions such as temperature or pressure vary. Order parameters often change sharply or continuously across these transitions.

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