2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184904We 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.latex file of 18 pages plus three ps figuresCondensed MatterHigh Energy Physics - LatticeHigh Energy Physics - Theorytext