  We consider a class of stochastic reaction-diffusion equations on the three
dimensional torus. The non-linearities are odd polynomials in the weakly
non-linear regime, and the smoothing mechanisms are very general higher order
perturbations of the Laplacian. The randomness is the space-time white noise
without regularisation. We show that these processes converge to the dynamical
$\Phi^4_3 (\lambda)$ model, where the coupling constant $\lambda$ has an
explicit expression involving non-trivial interactions between all details of
the smoothing mechanism and the non-linearity.
