Universality (physics)

The concept of universality is used in statistical mechanics in the context of continuous phase transitions and critical phenomena .

Universality here denotes the fact that certain properties of classes of systems depend only on a few system details: representatives of a universality class show quantitatively the same behavior (identical universal quantities), although they have a different crystal lattice , different interactions and other differences.

example

An example is the specific heat of liquids at constant volume (identical to the critical volume) near their critical temperature and the specific heat of Ising magnets near their Curie temperature . All of these specific heats diverge as a function of the deviation of the temperature from the critical temperature as with the same "universal" critical exponent . ${\ displaystyle T}$${\ displaystyle T _ {\ mathrm {c}}}$${\ displaystyle | T-T _ {\ mathrm {c}} | ^ {- \ alpha}}$ ${\ displaystyle \ alpha \ approx 0 {,} 11008}$

Besides the critical exponents (of which there are several), certain scale functions and amplitude ratios are also universal, e.g. B. the amplitude ratio of the specific heat at and . ${\ displaystyle T> T _ {\ mathrm {c}}}$${\ displaystyle T

The universality class in this example is that of the three-dimensional Ising magnet. It is characteristic of this example universality class that the spatial dimension and the dimension of the order parameter (the symmetry, here only a scalar ) determine the universality class to a significant extent. Two-dimensional Ising magnets or three-dimensional Heisenberg magnets (with a magnetization - Vector ) belong to other universality classes and have such. B. also other critical exponents.

history

All of this is the subject of the theory of critical phenomena that emerged in the 1970s. The term universality (Engl. Universality ) was Leo Kadanoff coined in the late 1970s, the concept is implicit but already in der Waals gas equation van and Landau's theory of phase transitions included.

Clear explanation

A clear explanation of universality is the scale invariance that exists at critical points of continuous phase transitions . All length scales contribute to the scale invariance larger than the lattice constant , many details on the atomic length scale become irrelevant. Technically and quantitatively, this fact is described with the help of field theories and the renormalization group .

This also applies to the dynamics in the vicinity of continuous phase transitions. Two systems can belong to the same universality class of statics and a different universality class of dynamics.

Occurrence

According to the general scheme of the renormalization group, universality can also be found in non-equilibrium systems , e.g. B. in reaction-diffusion models , with self-organized criticality or in the logistic equation , a very schematic iterated mathematical mapping (see also Feigenbaum constant ).