Eur. Phys. J. B 66, 271-278 (2008)
https://doi.org/10.1140/epjb/e2008-00417-1

Non-perturbative renormalization-group approach to lattice models

¹ Laboratoire de Physique Théorique de la Matière Condensée, CNRS – UMR 7600, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
² Laboratoire de Physique des Solides, CNRS – UMR 8502, Université Paris-Sud, 91405 Orsay, France
³ TCMP division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata, 700064, India
⁴ Theoretical Physics Department, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032, India

Corresponding author: ^a dupuis@lptmc.jussieu.fr

Received: 26 June 2008
Revised: 15 October 2008
Published online: 20 November 2008

Abstract

The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a φ⁴ theory defined on a d-dimensional hypercubic lattice. Within a simple approximation for the effective action, we solve the flow equations and obtain the renormalized dispersion ϵ(q) over the whole Brillouin zone of the reciprocal lattice. In the long-distance limit, where the lattice does not matter any more, we reproduce the usual flow equations of the continuum model. We show how the numerical solution of the flow equations can be simplified by expanding the dispersion in a finite number of circular harmonics.