Superinstantons and the Reliability of Perturbation Theory in Non-Abelian Models

In dimension $D\le 2$ the low temperature behavior of systems enjoying a continuous symmetry is dominated by superinstantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a superinstanton produces thermodynamic answers for the invariant Green's functions that differ from the standard ones, but only in non-Abelian models and only starting at $O(1/{\beta }^2)$. This effect modifies the $\beta$-function models and persists in the large $N$ limit of the $O\left(N\right)$ models.