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

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

2006-06-27

arxiv.org/abs/cond-mat/0606698v3

Physics

Condensed Matter

Statistical Mechanics

19 pages, 20 figures. Minor corrections

Scientific paper

10.1103/PhysRevB.74.214419

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.

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