Criticality

At the critical point, a number of important events occur, regardless of the nature of the material. Physicists gain enormous insight when studying a material undergoing a phase transition at its critical point. At the critical point the material exhibits an important property calledPerhaps the most important property is the development of long range order. The previously disordered system, with no correlation between the interacting atoms, develops high correlation. In a disordered magnet the spins are pointing in every direction, and thus on average the material has no magnetization. Below the Curie temperature all the spins are aligned and the magnet has a finite magnetization. Similarly, the molecules in a liquid crystal are randomly oriented, but below the transition temperature align. Liquid crystals have a second phase transition where in addition to being aligned orientationally (pointing in the same direction) also align spatially (sit next to one another in a regular ordered fashion).

When a system transitions from one phase to another, it loses or gains

When the symmetry is lost, it can be said that it is replaced by a

A spin wave is the slow variation of the magnetic dipoles in an ordered magnetic material. This is the low temperature excitation that emerges in the ordered phase.

A phase transition is also marked by the appearance of an

An important attribute of phase transitions is the divergence of certain thermodynamic properties at the critical point. Divergence means that the thermodynamic property suffers a discontinuity and changes drastically from its value in the disordered state. This is qualitatively related to the appearance of long range order, and by measuring the values of these thermodynamic variables during the phase transition, many important properties of the transition can be assessed.

This is an example of the divergence of the heat capacity when a material undergoes a phase transition. The rate at which the heat capacity changes with temperature near the phase transition gives important insight into the nature of the phase transition and its relation to transitions in the same universality class.

The divergence of thermodynamic properties like the susceptibility and the correlation length are related to the

The divergence of thermodynamic quantities is of particular importance as the divergence has a singular dependence on temperature of the form

Where alpha is a positive constant. Many materials will have the same constant and diverge the same way with temperature. This is another example of universality.

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