The summability of the 1/N expansion in a simplified O(N) model

The authors discuss the 1/N expansion of an O(N) quartic single-mode model. The imposition of boundary conditions by the 1/N expansion is explicitly displayed, using the exact solutions. In particular, it is shown that in the negative mass case the 1/N expansion is Borel summable whereas the lambda (and h(cross)) expansions are not. The applicability of these results to more realistic models (i.e. as the first term of a strong coupling approximation scheme) is discussed.