  We consider a class of gauge invariant models on the noncommutative space
$\mathbb{R}^3_\lambda$, a deformation of $\mathbb{R}^3$. Focusing on massless
models with no linear $A_i$ dependence, we obtain noncommutative gauge models
for which the computation of the propagator can be done in a convenient gauge.
We find that the infrared singularity of the massless propagator disappears in
the computation of the correlation functions. We show that massless gauge
invariant models on $\mathbb{R}^3_\lambda$ have quantum instabilities of the
vacuum, signaled by the occurrence of non vanishing 1-point functions for some
but not all of the components of the gauge potential. The tadpole contribution
to the effective action cannot be interpreted as a standard $\sigma$-term. Its
global symmetry does not fit with the one of the classical action, reminiscent
to an explicit global symmetry breaking term.
