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

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.

arXiv admin note: substantial text overlap with arXiv:1207.4014

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• A general method for calculating lattice Green functions on the branch cut