The renormalization group: Critical phenomena and the Kondo problem

Several topics involving renormalization group ideas are reviewed. The solution of the s-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in detail. ''Block spin'' methods, applied to the two dimensional Ising model, are explained. A relatively short review of basic renormalization group ideas is given, mainly in the context of critical phenomena. The relationship of the modern renormalization group to the older problems of divergences in statistical mechanics and field theory and field theoretic renormalization is discussed. The special case of ''marginal variables'' is discussed in detail, along with the relationship of the modern renormalization group to its original formulation by Gell-Mann and Low and others