Variational principles,renormalization group,and Kadanoff's universality

Variational principles satisfied by various thermodynamic functionals are used to set up a completely renormalized scheme for the analysis of critical phenomena. Different aspects of Kadanoff's universality can be expressed in a simple fashion in our language. The main result of the paper is a unified derivation of the scaling laws combining the variational principles with renormalization group techniques which are especially simple in this formalism. A suitable choice of the normalization point has led to a new renormalization group transformation. The corresponding differential equation can be solved even in the nonasymptotic region. The discussion of the asymptotic theory and of the approach to it is therefore simpler. The connection with the more traditional approaches is discussed. The calculation of the critical indices is reduced to only two of them which are directly expressed in terms of renormalized quantities. From this point onwards their evaluation proceeds along standard lines. Special emphasis has been given to the illustration of the power and conceptual simplicity of the method.