Critical line of the $Φ^4$ theory on a simple cubic lattice in the local potential approximation

Jean-Michel Caillol

doi:10.1016/j.nuclphysb.2012.07.032

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arXiv · 1207.4014

Critical line of the $Φ^4$ theory on a simple cubic lattice in the local potential approximation

Jean-Michel Caillol

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Abstract

We establish the critical line of the one-component $Φ^4$ (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.

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Jean-Michel Caillol. 2012-08-22. Critical line of the $Φ^4$ theory on a simple cubic lattice in the local potential approximation. https://doi.org/10.1016/j.nuclphysb.2012.07.032

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