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 epsilon(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.
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The estimates of \(\tilde\rho_0(t=0)\) and \(\tilde\lambda(t=0)\) based on the continuum model flow equations run backwards in "time" from t=-16 (green lines in Figs. 2 and 3) are given by 75 and 0.38, respectively
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Dupuis, N., Sengupta, K. Non-perturbative renormalization-group approach to lattice models. Eur. Phys. J. B 66, 271–278 (2008). https://doi.org/10.1140/epjb/e2008-00417-1
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DOI: https://doi.org/10.1140/epjb/e2008-00417-1