ABSTRACT
This chapter shows that mean field theory in its simplest form can be improved by inclusion of Gaussian fluctuations. The transition temperature is shifted, and the heat capacity does indeed exhibit a divergence rather than the discontinuity predicted for a uniform system. The expansion, in which the Gaussian and mean field theories are the lowest terms, has an expansion parameter which diverges as the critical point is approached. The problem of anomalous dimensions in critical phenomena was discovered and solved apparently without knowledge or recognition of these other phenomena exhibiting case asymptotics. The chapter briefly discusses the notion of renormalisation in field theory. It is an interesting historical point that Landau had first-hand knowledge of anomalous dimensions in both critical phenomena and the problem of the converging shock wave, but apparently made no reference to a connection between them.
