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

TL;DR

This paper evaluates the reliability of the Optimized Perturbation Theory (OPT) in a 0-dimensional $O(N)$ scalar field model, demonstrating its stability and improved convergence over traditional methods across various optimization schemes.

Contribution

The study systematically compares OPT with exact results, $1/N$-expansion, and perturbation theory, highlighting OPT's superior stability and convergence in the model.

Findings

OPT results are stable at large couplings.

OPT shows better convergence than $1/N$-expansion.

Minimal sensitive optimization improves results, especially for self-energy.

Abstract

We address the reliability of the Optimized Perturbation Theory (OPT) in the context of the 0-dimensional $O(N)$ scalar field model. The effective potential, the self-energy and the 1PI four-point Green's function for the model are computed using different optimization schemes and the results contrasted to the exact results for the model. Our results are also compared to those obtained with the $1/N$-expansion and with those from ordinary perturbation theory. The OPT results are shown to be stable even at large couplings and to have better convergence properties than the ones produced in the $1/N$-expansion. It is also shown that the principle of minimal sensitive optimization procedure used in conjunction with the OPT method tends to always produce better results, in particular when applied directly to the self-energy.