Editing Phase transition (section)

===Order parameters<!--'Order parameter' and 'Order parameters' redirect here-->===
An '''order parameter'''<!--boldface per WP:R#PLA--> is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other.<ref>{{cite journal |last1=Clark |first1=J.B. |last2=Hastie |first2=J.W. |last3=Kihlborg |first3=L.H.E. |last4=Metselaar |first4=R. |last5=Thackeray |first5=M.M. |title=Definitions of terms relating to phase transitions of the solid state |journal=Pure and Applied Chemistry |date=1994 |volume=66 |issue=3 |pages=577–594 |doi=10.1351/pac199466030577 |s2cid=95616565 |doi-access=free }}</ref> At the critical point, the order parameter [[susceptibility (disambiguation)|susceptibility]] will usually diverge.

An example of an order parameter is the net [[magnetization]] in a [[ferromagnetic]] system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities.

From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the [[ferromagnetic]] phase, one must provide the net [[magnetization]], whose direction was spontaneously chosen when the system cooled below the [[Curie point]]. However, note that order parameters can also be defined for non-symmetry-breaking transitions.{{cn|date=December 2023}}

Some phase transitions, such as [[superconductivity|superconducting]] and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition.{{citation needed|date=August 2022}}

There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as [[Quantum vortex|vortex]]- or [[Topological defect|defect]] lines.