The stability of the O invariant fixed point in three dimensions

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 known that there is a critical value below which the O(N) fixed point is stable and above which the cubic fixed point becomes the stable one. Whilst we cannot exclude that , as recently claimed, our analysis strongly suggests that coincides with 3.