Renormalization group

Summary

The renormalization group is a family of transformations that average out the short-distance details of a system and rescale lengths. Each transformation maps a Hamiltonian to an effective one. Repeating the transformation follows a flow in the space of couplings. Critical points correspond to fixed points of this flow, and the eigenvalues of the linearized flow there give the critical exponents. It explains scaling and universality, and in quantum field theory it describes how couplings change with the energy scale.