Fixed point of the renormalization group

Summary

A fixed point of the renormalization group is a Hamiltonian, or a set of coupling constants, that a renormalization group transformation maps to itself. Since such a transformation divides the correlation length by the scale factor, a fixed point has correlation length $0$ or $\infty$. Fixed points with infinite correlation length describe critical points, and the flow near them determines the critical exponents. All models that flow to the same fixed point form one universality class.