Phase transition#Order parameters

Order parameter used to describe the state of a system during a phase transition.

During the transition from a liquid phase to a crystalline solid phase, the system passes from a high symmetry ( isotropy and homogeneity ) to a phase, wherein this symmetry is broken ( leaving only the lattice symmetry of the crystal). This is a parameter that is in the liquid phase 0 and in the crystalline phase assumes a finite value, a measure of the order of a physical system, which the concept of order parameter explains: A higher value corresponds to stronger order, whereas disorder at 0 is present.

However, it also referred to the case of phase transitions without symmetry breaking parameter, with which the transition is described as an order parameter. For example, the volume fraction of the liquid is a suitable order of parameters to describe the transition from liquid to gas ( at a sufficiently low pressure, ie, not in the vicinity of the triple point ). In the gaseous state it is 0, in the liquid just the first

The description of order parameters can, however, also be applied to systems that continuously change their order within a phase.

Depending on the type of the phase transition, the order parameter abruptly accept a new value and thus serve directly as an indication of the phase transition or change constantly. In a physical system, there are often multiple effects, suggesting the order. From the physical quantities that are represented in these effects, choose the one size, from which one calculates the order parameter.

There are also vectorial order parameter possible. Their use is useful for order changes to the isotropy of the system. There, in the ordered phase, a direction is excellent. The vector used then has this direction and amount as the strength of the alignment of the individual components in the preferred direction.

Related to the symmetry

Use find order parameters in statistical physics, studied the phase transitions with spontaneous symmetry breaking. There corresponds to the additional degree of freedom, the symmetry breaking releases, just with the order parameter. One example is the spontaneous magnetization of a ferromagnet upon cooling. It occurs as an additional degree of freedom of the system to the magnetization and changes to small jumps continuously from 0 to the final full magnetization of the ferromagnet. An example of an order parameter does not correspond to the new degree of freedom of the system after the phase transition is to use the density for the description of the liquid-gas transition.


Other examples of order parameters are:

  • The magnetization in the phase transition from ferromagnetism to paramagnetism.
  • In the semiconductor, the charge carrier density in the transition from the insulator to conductive state.
  • In the Landau - Ginzburg theory corresponds to the order parameter of the wave function and thus can be complex and vary spatial. The square of the wavefunction gives the density of Cooper pairs.

Continuous change of the order parameter

A striking example of multiple phases and continuous order changes are liquid crystals. Their different phases, between which you can switch are classified differently. The ordered phases differ in the orientation of regions of parallel alignment of the rod-shaped crystals. Within such a phase, slight variations of the parallelism of the crystals can occur, which can be summed up by an angle-dependent order parameter. However, there is also a random phase, in which the crystals are oriented along random directions.

Jumping order parameter

Transitions between phases which are different states of matter, change the order of the system by leaps and bounds. The largest (in terms of the density as an order parameter ), this effect is produced in the sublimation of crystalline solids and its inverse, the Resublimation. Between the gas with a very low density, and the solid having a considerably greater, the system does not assume a state intermediate density. It also corresponds to the intuitive idea that a regular crystal lattice is more ordered than the randomly distributed molecules of a gas. In mathematical terms, has ordered crystalline translational symmetry. A step to the distance between the atoms of the lattice along again leads to an identical location ( an atom surrounded by the other at the same distance ). In the gas, however, this translational symmetry is broken and a fixed step size happens to run both on empty seats as well as to other gas molecules.