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

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).