Many condensed matter systems undergo transitions from one phase to another driven by many parameters such as magnetic or electric field, pressure, temperature, chemical composition and other thermodynamic variables. Phase transitions induce a change in the entropy of the system. The phase transitions can be characterized by the symmetry principle. For instance, for a melting process, the crystal solid holds a specific crystalline symmetry, while its liquid phase is spherically symmetric. Therefore, there is no symmetry relationship between the solid and liquid, and thus no continuous transition from the solid to liquid. In equilibrium cases, we have either a solid or a liquid, or a mixture of the two phases, but there is no state at which the phases of the solid and liquid are symmetry-indistinguishable.

The phase changes can be:
         i) Discontinuous, first order phase transition.
         ii) Continuous, second order transition.

As an example, the transition temperatures of BaTiO₃ are given by,

Table 1781. Special phase transitions induced specific crystal properties.