Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

Details Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy Functional renormalization group in the broken symmetry phase: momentum dependence and two-parameter scaling of the self-energy

2007-07-27

arxiv.org/abs/0707.4110v2

J. Phys. Condens. Matter 20, 075208 (2008)

Physics

Condensed Matter

Statistical Mechanics

9 pages, 4 figures, puplished version

Scientific paper

10.1088/0953-8984/20/7/075208

We include spontaneous symmetry breaking into the functional renormalization group (RG) equations for the irreducible vertices of Ginzburg-Landau theories by augmenting these equations by a flow equation for the order parameter, which is determined from the requirement that at each RG step the vertex with one external leg vanishes identically. Using this strategy, we propose a simple truncation of the coupled RG flow equations for the vertices in the broken symmetry phase of the Ising universality class in D dimensions. Our truncation yields the full momentum dependence of the self-energy Sigma (k) and interpolates between lowest order perturbation theory at large momenta k and the critical scaling regime for small k. Close to the critical point, our method yields the self-energy in the scaling form Sigma (k) = k_c^2 sigma^{-} (k | xi, k / k_c), where xi is the order parameter correlation length, k_c is the Ginzburg scale, and sigma^{-} (x, y) is a dimensionless two-parameter scaling function for the broken symmetry phase which we explicitly calculate within our truncation.

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