  We establish the critical line of the one-component $\Phi^4$ (or
Landau-Ginzburg) model on a simple four dimensional cubic lattice. Our study is
performed in the framework of the non-perturbative renormalization group in the
local potential approximation with a soft infra-red regulator. The transition
is found to be of second order even in the Gaussian limit where first order
would be expected according to some recent theoretical predictions.
