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arXiv:0712.3556 · Physical Review B

Nonperturbative functional renormalization group for random field models and related disordered systems. II. Results for the random field O(N) model

Matthieu Tissier, Gilles Tarjus

Published Jul 9, 2008• 66 citations
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Abstract

We study the critical behavior and phase diagram of the $d$-dimensional random field $O(N)$ model by means of the nonperturbative functional renormalization group approach presented in the preceding paper. We show that the dimensional-reduction predictions, which are obtained from conventional perturbation theory, break down below a critical dimension ${d}_{\text{DR}}(N)$ and we provide a description of criticality, ferromagnetic ordering, and quasi-long range order in the whole $(N,d)$ plane. Below ${d}_{\text{DR}}(N)$, our formalism gives access to both the typical behavior of the system, which is controlled by zero-temperature fixed points at which the effective action has a nonanalytic field dependence, and to the physics of rare low-energy excitations (``droplets''), which is described at nonzero temperature by the rounding of the nonanalyticity in a thermal boundary layer.

DOI
10.1103/physrevb.78.024204

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