Fixed points and their stability in the functional renormalization group of random field models

Abstract

We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of the $(N,d)$ plane where one passes from a critical behavior satisfying the $d\to d-2$ dimensional reduction to one where it breaks down due to the appearance of strong enough nonanalyticities in the functional dependence of the cumulants of the renormalized disorder. We unveil an intricate and unusual behavior.

11 pages, 11 figures

References in corpus (2)

• Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models
• Stability of fixed points in the (4+ε)-dimensional random field O(N) spin model for sufficiently large N

Cited by in corpus (8)

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• Critical behavior of the random-field Ising model with long-range interactions in one dimension
• Dimensional reduction breakdown and correction to scaling in the random-field Ising model
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• One-loop functional renormalization group study for the dimensional reduction and its breakdown in the long-range random field O($N$) spin model near lower critical dimension