# Universality

## Definition

The term universality is used in different fields of physics to describe the observation that many systems show properties that are independent of the detailed dynamic interactions between its constitutive elements. This specific formulation of universality is derived from statistical mechanics, where universality usually results from a scaling for a very large number of interacting particles. Universality is basically the physical equivalent of the everyday observation that from very far away (e.g. our macroscopic standpoint) many things that are in fact different (e.g. dynamic interactions vary) look the same (have the same properties).

## Origin

This intuitive notion is generalized in the concept of the renormalization group. Operators (i.e. perturbations to the energy or time scale) are classified into ones that affect the continuum limit and ones that don't. This is done by obvserving the value of an observable while the system undergoes a renormalization transformation (basically zooming out of the system). If the observable always increases during the transformation it is called relevant and will be needed to describe the macroscopic behavior. Applying this mechanism leads to two main results. While the number of microscopic variables is always on the order of <math>10^{23}</math> the number of relevant observables is nearly always a very small number. Secondly many seemingly unrelated problems have the same set of relevant observables, they belong to the same universality class.

## Examples in soft matter

- Diffusion-limited aggregation of colloidal structures
- Second order phase transition in complex fluids
- Reaction-limited colloid aggregation
- Percolation

## References

- R. Jones, "Soft Condensed Matter," Oxford University Press Inc., New York (2002).
- T. Witten, "Structured Fluids: Polymers, Colloids, Surfactants," Oxford University Press Inc., New York (2004).
- http://en.wikipedia.org/wiki/Universality_%28dynamical_systems%29
- http://en.wikipedia.org/wiki/Renormalization_group

See also: Percolation