Large scale behaviour of 3D continuous phase coexistence models

We study a class of three dimensional continuous phase coexistence models, and show that, under different symmetry assumptions on the potential, the large-scale behaviour of such models near a bifurcation point is described by the dynamical $\Phi^p_3$ models for $p \in \{2,3,4\}$. This result is specific to space dimension $3$ and does not hold in dimension $2$.