The order parameter is normally a quantity which is zero in one phase (usually above the critical point), and non-zero in the other. It characterises the onset of order at the phase transition. The order parameter susceptibility will usually diverge approaching the critical point. For a ferromagnetic system undergoing a phase transition, the order parameter is the net magnetization. For liquid/gas transitions, the order parameter is the difference of the densities.
When symmetry is broken, 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. Such variables are examples of order parameters. An order parameter is a measure of the degree of order in a system; it ranges between zero for total disorder and the saturation value for complete order. For example, an order parameter can indicate the degree of order in a liquid crystal. However, note that order parameters can also be defined for non-symmetry-breaking transitions. Some phase transitions, such as 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.
There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as vortex- or defect lines.
Famous quotes containing the words order and/or parameters:
“Life has no meaning unless one lives it with a will, at least to the limit of ones will. Virtue, good, evil are nothing but words, unless one takes them apart in order to build something with them; they do not win their true meaning until one knows how to apply them.”
—Paul Gauguin (18481903)
“What our children have to fear is not the cars on the highways of tomorrow but our own pleasure in calculating the most elegant parameters of their deaths.”
—J.G. (James Graham)