  Using the renormalization group improvement technique, we study the effective
potential of a model consisting of $N$ scalar fields $\phi^i$ transforming in
the fundamental representation of $O(N)$ group coupled to an additional scalar
field $\sigma$ via cubic interactions, defined in a six-dimensional spacetime.
We find that the model presents a metastable vacuum, that can be long-lived,
where the particles become massive. The existence of attractive and repulsive
interactions plays a crucial role in such phenomena.
