Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models

Abstract

We study by the perturbative Functional Renormalization Group (FRG) the Random Field and Random Anisotropy O(N) models near $d=4$, the lower critical dimension of ferromagnetism. The long-distance physics is controlled by zero-temperature fixed points at which the renormalized effective action is nonanalytic. We obtain the beta functions at 2-loop order, showing that despite the nonanalytic character of the renormalized effective action, the theory is perturbatively renormalizable at this order. The physical results obtained at 2-loop level, most notably concerning the breakdown of dimensional reduction at the critical point and the stability of quasi-long range order in $d<4$, are shown to fit into the picture predicted by our recent non-perturbative FRG approach.

19 pages, 20 figures. Minor corrections

References in corpus (1)

• Stability of fixed points in the (4+ε)-dimensional random field O(N) spin model for sufficiently large N

Cited by in corpus (2)

• Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
• Long-range correlated random field and random anisotropy O(N) models: A functional renormalization group study