Large-order behaviour of the 1/N expansion in zero and one dimensions

Abstract

The large-order behaviour of the 1/N expansion in the zero- and one-dimensional g phi ⁴ model is investigated. The one-dimensional N-vector model is also considered. The asymptotic behaviour shows oscillations due to complex instantons. The phase and the amplitude of these leading behaviours are determined theoretically and are compared with the explicit numerical calculations of higher orders. In the one-dimensional g phi ⁴ model the relevance of the large-N instanton is discussed.