The state of different condensed matter systems is characrerized by different quantities: density, symmetry of a crystal, magnetization, electric polarization, etc. Many such states can have a certain ordering. Different types of ordering can be characterized by order parameters.
Examples of order parameters are, for instance: for ferromagnets – the magnetization M; for ferroelectrics – the polarization P; for structural phase transitions – the distortion uαβ, etc. Typically the system is disordered at high temperatures, and certain types of ordering may appear with decreasing temperature. This is clear already from the general expressions for thermodynamic functions, see Chapter 1: at finite temperatures the state of the system is chosen by the condition of the minimum of the corresponding thermodynamic potential, the Helmholtz free energy (1.8) or the Gibbs free energy (1.10), and from those expressions it is clear that with increasing temperature it is favourable to have the highest entropy possible, i.e. a disordered state. But some types of ordering are usually established at lower temperatures, where the entropy does not play such an important role, and the minimum of the energy is reached by establishing that ordering.
The general order parameter η depends on temperature, and in principle also on other external parameters – pressure, magnetic field, etc. Typical cases of the dependence of the order parameter on temperature are shown in Fig. 2.1.