Effective potential in three-dimensional O(N) models

TL;DR

This paper analyzes the effective potential in three-dimensional O(N) models, estimating higher-order couplings using epsilon-expansion and known exact results, and compares these with other approaches.

Contribution

It provides new estimates for six- and eight-point couplings in 3D O(N) models, incorporating exact lower-dimensional results and high-temperature data for N=1.

Findings

Estimated renormalized couplings for N=0,1,2,3

Compared estimates with other theoretical approaches

Extended analysis to two-dimensional O(N) models

Abstract

We consider the effective potential in three-dimensional models with O(N) symmetry. For generic values of N, and in particular for the physically interesting cases N=0,1,2,3, we determine the six-point and eight-point renormalized coupling constants which parametrize its small-field expansion. These estimates are obtained from the analysis of their $\epsilon$-expansion, taking into account the exact results in one and zero dimensions, and, for the Ising model (i.e. N=1), the accurate high-temperature estimates in two dimensions. They are compared with the available results from other approaches. We also obtain corresponding estimates for the two-dimensional O($N$) models.