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Two-loop Functional Renormalization Group of the Random Field and Random Anisotropy O(N) Models | | Matthieu Tissier
; Gilles Tarjus
; | | Date: |
27 Jun 2006 | | Subject: | Statistical Mechanics; Disordered Systems and Neural Networks | | 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. | | Source: | arXiv, cond-mat/0606698 | | Services: | Forum | Review | PDF | Favorites | |
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