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We address the reliability of the Optimized Perturbation Theory (OPT) in thecontext of the 0-dimensional $O(N)$ scalar field model. The effectivepotential, the self-energy and the 1PI four-point Green's function for themodel are computed using different optimization schemes and the resultscontrasted to the exact results for the model. Our results are also compared tothose obtained with the $1/N$-expansion and with those from ordinaryperturbation theory. The OPT results are shown to be stable even at largecouplings and to have better convergence properties than the ones produced inthe $1/N$-expansion. It is also shown that the principle of minimal sensitiveoptimization procedure used in conjunction with the OPT method tends to alwaysproduce better results, in particular when applied directly to the self-energy.

Reliability of the optimized perturbation theory in the 0-dimensional $O(N)$ scalar field model