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 $d_{DR}$.

References in corpus (4)

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Cited by in corpus (5)

• The fate of Parisi-Sourlas supersymmetry in Random Field models
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Thermal vestiges of avalanches in the driven random field Ising model
• On the breakdown of dimensional reduction and supersymmetry in random-field models