The stability of the O(N) invariant fixed point in three dimensions

TL;DR

This paper investigates the stability of the O(N) fixed point in three dimensions for N=2, 3, 4 using Monte Carlo simulations and finite size scaling, suggesting the critical N value for stability is likely 3.

Contribution

The study provides high-precision numerical evidence that the critical N value for stability of the O(N) fixed point is approximately 3, clarifying a debated point in phase transition theory.

Findings

N_c likely equals 3, indicating stability for N<3 and instability for N>3.

Monte Carlo simulations support the stability boundary at N=3.

High-precision analysis refutes the possibility that N_c<3.

Abstract

We study the stability of the O(N) fixed point in three dimensions under perturbations of the cubic type. We address this problem in the three cases $N=2,3,4$ by using finite size scaling techniques and high precision Monte Carlo simulations. It is well know that there is a critical value $2<N_c<4$ below which the O(N) fixed point is stable and above which the cubic fixed point becomes the stable one. While we cannot exclude that $N_c<3$, as recently claimed by Kleinert and collaborators, our analysis strongly suggests that $N_c$ coincides with 3.