Super-Instantons and the Reliability of Perturbation Theory in Non-Abelian Models

Abstract

In dimension $D\le 2$ the low temperature behavior of systems enjoying a continuous symmetry is dominated by super-instantons: classical configurations of arbitrarily low energy. Perturbation theory in the background of a super-instanton 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 of the $O(N)$ models and persists in the large $N$ limit of the $O(N)$ models.

8 pages, plain LaTeX, MPI-Ph/93-87 and AZPH-TH/93-33

References in corpus (2)

• The Difference between Abelian and Non-Abelian Models: Fact and Fancy
• Existence of Algebraic Decay in Nonabelian Ferromagnets

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