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

Abstract

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 $d_{DR}$.