Scaling concepts play a central role in the analysis of the ever more complex systems which nowadays are the focus of much attention in the physical sciences. Whether these problems relate to the very large scale structure of the universe, to the complicated forms of everyday macroscopic objects, or to the behaviour of the interactions between the fundamental constituents of matter at very short distances, they all have the common feature of possessing large numbers of degrees of freedom which interact with each other in a complicated and highly non-linear fashion, often according to laws which are only poorly understood. Yet it is often possible to make progress in understanding such problems by isolating a few relevant variables which characterise the behaviour of these systems on a particular length or time scale, and postulating simple scaling relations between them. These may serve to unify sets of experimental and numerical data taken under widely differing conditions, a phenomenon called universality. When there is only a single independent variable, these relations often take the form of power laws, with exponents which do not appear to be simple rational numbers yet are, once again, universal.

The existence of such scaling behaviour may often be explained through a framework of theoretical ideas loosely grouped under the term renormalization. Roughly speaking, this describes how the parameters specifying the system must be adjusted, under putative changes of the underlying dynamics, in such a way as not to modify the measurable properties on the length or time scales of interest.