2007/07/31 by Andreas Sinner, N. Hasselmann, Nils Hasselmann +1
Mathematics · Physics and Astronomy · #Critical phenomena #Critical point (mathematics) #Functional renormalization group #Geometry #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Renormalization #Renormalization group #Scaling #Symmetry breaking #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/0953-8984/20/7/075208
published as J. Phys. Condens. Matter 20, 075208 (2008) · 9 pages, 4 figures, puplished version
openalex publication_date 2008/01/25 · arxiv created 2008/07/09 · arxiv updated 2011/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We include spontaneous symmetry breaking in the functional renormalization group 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 renormalization group (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 Σ( 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 Σ( k ) = k c 2 σ − (| k |ξ,| k |/ k c ), where ξ is the order parameter correlation length, k c is the Ginzburg scale, and σ − ( x , y ) is a dimensionless two-parameter scaling function for the broken symmetry phase which we calculate explicitly within our truncation.