Effective Action Method for Computing Next to Leading Corrections of $O(N)$ Models

TL;DR

This paper develops a method to compute next-to-leading order corrections in the 1/N expansion for the effective potential of N-component Ginzburg-Landau models with spontaneous symmetry breaking, extending the Self-Consistent Screened Approximation.

Contribution

It introduces a generalized approach to calculate higher-order corrections in the 1/N expansion for Ginzburg-Landau models, improving upon existing approximation methods.

Findings

Derived next-to-leading order corrections for the effective potential.

Extended the Self-Consistent Screened Approximation to a broader class of models.

Provided a systematic method for analyzing spontaneous symmetry breaking in large N systems.

Abstract

We compute the corrections of next to leading order in the ${1 \over N}$ expansion to the effective potential of a system described by a Ginzburg-Landau model with $N$ components and quartic interaction, in the case of spontaneous symmetry breaking. The method we apply allows to generalize in a simple way the so-called Self-Consistent Screened Approximation (SCSA).