Critical line of the Φ4 theory on a simple cubic lattice in the local potential approximation

We establish the critical line of the one-component Φ4 (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 [M. Hasenbusch, J. Phys. A: Math. Gen. 32 (1999) 4851] with a relative error of, at worst, ∼3⋅10−3 on published points (critical parameters) of this line.