The Expansion and Universality in Three Dimensions

It has been observed that the classification into universality classes of critical behavior, as established by perturbative renormalization group in the vicinity of four or six dimensions of space by the epsilon expansion, remains valid down to three dimensions in all known cases, even when perturbative renormalization group fails in lower dimensions. In this paper we argue that this classification into universality classes remains true in lower dimensions of space, even when perturbative renormalization group fails, because of the well known phenomenon of eigenvalue repulsion.