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

M. Caselle·M. Hasenbusch
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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.

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M. Caselle, M. Hasenbusch. 1997-11-10. The stability of the O(N) invariant fixed point in three dimensions. https://doi.org/10.1088/0305-4470%2F31%2F20%2F004

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