Dimensional reduction breakdown and correction to scaling in the random-field Ising model

• Published in: arXiv.org
• Main Authors: Balog, Ivan, Tarjus, Gilles, Tissier, Matthieu
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 31.08.2020
• Subjects: Computer simulation; Ising model; Physics - Disordered Systems and Neural Networks; Reduction; Scaling; Supersymmetry
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2008.13650

We provide a theoretical analysis by means of the nonperturbative functional renormalization group (NP-FRG) of the corrections to scaling in the critical behavior of the random-field Ising model (RFIM) near the dimension \(d_{DR}\approx 5.1\) that separates a region where the renormalized theory at the fixed point is supersymmetric and critical scaling satisfies the \(d\to d-2\) dimensional reduction property (\(d>d_{DR}\)) from a region where both supersymmetry and dimensional reduction break down at criticality (\(d<d_{DR}\)). We show that the NP-FRG results are in very good agreement with recent large-scale lattice simulations of the RFIM in \(d=5\) and we detail the consequences for the leading correction-to-scaling exponent of the peculiar boundary-layer mechanism by which the dimensional-reduction fixed point disappears and the dimensional-reduction-broken fixed point emerges in \(d_{DR}\).