  We establish the critical line of the one-component $\Phi^4$ (or
Landau-Ginzburg) model on the simple cubic lattice in three dimensions. Our
study is performed in the framework of the non-perturbative renormalization
group in the local potential approximation. Soft as well as ultra-sharp
infra-red regulators are both considered. While the latter gives poor results,
the critical line given by the soft cut-off compares well with the Monte Carlo
simulations data of Hasenbusch (J. Phys. A : Math. Gen. 32 (1999) 4851) with a
relative error of, at worst, $\sim 3. 10^{-3}$ on published points (critical
parameters) of this line.
