2004/10/31 by Gilles Tarjus, Matthieu Tissier · 2 citations
Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.93.267008
published as Physical Review Letters 93 (2003) 267008 · 4 pages, 2 figures, Revtex4, minor corrections
openalex publication_date 2004/12/23 · arxiv created 2005/01/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a nonperturbative functional renormalization group approach for the random-field O(N) model that allows us to investigate the ordering transition in any dimension and for any value of N including the Ising case. We show that the failure of dimensional reduction and standard perturbation theory is due to the nonanalytic nature of the zero-temperature fixed point controlling the critical behavior, nonanalyticity, which is associated with the existence of many metastable states. We find that this nonanalyticity leads to critical exponents differing from the dimensional reduction prediction only below a critical dimension dc(N)<6, with dc(N=1)>3.