2006/06/30 by Matthieu Tissier, Gilles Tarjus · 1 citation
Physics and Astronomy · #NMR spectroscopy and applications #Physics of Superconductivity and Magnetism #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.74.214419
19 pages, 20 figures. Minor corrections
arxiv created 2006/07/20 · openalex publication_date 2006/12/18 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study by the perturbative functional renormalization group (FRG) the random field and random anisotropy O(N) models near d=4, the lower critical dimension of ferromagnetism. The long-distance physics is controlled by zero-temperature fixed points at which the renormalized effective action is nonanalytic. We obtain the beta functions at two-loop order, showing that despite the nonanalytic character of the renormalized effective action, the theory is perturbatively renormalizable at this order. The physical results obtained at the two-loop level, most notably concerning the breakdown of dimensional reduction at the critical point and the stability of quasi-long-range order in d<4, are shown to fit into the picture predicted by our recent nonperturbative FRG approach.