Relevant and irrelevant operators

Summary

Near a fixed point of the renormalization group, a small perturbation of the couplings either grows or shrinks under repeated coarse-graining. Perturbations that grow are called relevant, those that shrink are called irrelevant, and those that neither grow nor shrink to first order are called marginal. The relevant directions are the parameters one must tune to reach a critical point, such as the temperature and the magnetic field of a magnet. Their growth rates give the critical exponents, and the irrelevant directions explain universality.