Probabilistic approach to the Widom-Kadanoff scaling relations

The fourth-order term in the Ginzburg-Landau free-energy functional tends to suppress large excursions of the order parameter. The probability distribution of the fluctuations of the order parameter integrated over a volume of size comparable to the correlation length is therefore not Gaussian. A similarity principle applied to the non-Gaussian shape parameters yields three of the familiar Widom-Kadanoff scaling relations.