Critical line of the $\Phi^4$ scalar field theory on a 4D cubic lattice in the local potential approximation

TL;DR

This paper determines the critical line of the four-dimensional $\

Contribution

It applies the non-perturbative renormalization group in the local potential approximation to accurately identify the critical line of the 4D $\

Findings

The transition is second order even in the Gaussian limit.

The critical line is precisely established on a 4D cubic lattice.

Contradicts some recent predictions of first-order transition.

Abstract

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.