Non-perturbative renormalization-group approach to lattice models

Details Non-perturbative renormalization-group approach to lattice models Non-perturbative renormalization-group approach to lattice models

2008-06-26

arxiv.org/abs/0806.4257v2

Eur. Phys. J. B 66, 271 (2008)

Physics

Condensed Matter

Statistical Mechanics

v1) 8 pages, 7 figures, v2) includes a discussion of the Ginzburg scale vs. the lattice scale

Scientific paper

10.1140/epjb/e2008-00417-1

The non-perturbative renormalization-group approach is extended to lattice models, considering as an example a $\phi^4$ 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 $\eps(\q)$ 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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