ABSTRACT
This chapter shows that anomalous dimensions reflect the presence of a microscopic length scale, which affects the behaviour of thermodynamic and correlation functions asymptotically close to the critical point. It explains the calculation of anomalous dimensions by renormalisation group techniques taking as our examples certain non-linear diffusion problems that arise in fluid dynamics. Despite the apparent dissimilarity between critical phenomena and fluid flow far from equilibrium, the techniques involved in calculating anomalous dimensions are actually identical. The chapter provides a physical explanation of renormalisation, in its most general context. There are two distinct steps in applying renormalisation and renormalisation group methods to a given problem. The first step is an extension of dimensional analysis, taking into account renormalisation effects. The second step is to combine the RG with an approximation scheme, such as perturbation theory, in order to estimate the values of the anomalous dimensions.
