  We analyze the static potentials for various representations in SU($3$)
Yang-Mills theory within the framework of the domain model of center vortices.
The influence of vortex interactions is investigated on the static potentials.
We show that, by ad-hoc choosing the probability weights of the different
vortex configurations contributing to the static potential, a
phenomenologically satisfactory result for the different representations can be
achieved. In particular including vacuum domains, a way to effectively
parametrize vortex interactions, is crucial in obtaining an (almost) everywhere
convex potential when interpolating between the short distances and the
asymptotic regimes.
