Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-12-20
Phys. Rev. B 78, 024204 (2008)
Physics
Condensed Matter
Statistical Mechanics
20 pages, 7 figures
Scientific paper
10.1103/PhysRevB.78.024204
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, obtained from conventional perturbation theory, break down below a critical dimension $d_{DR}(N)$ and we provide a description of criticality, ferromagnetic ordering and quasi-long range order in the whole $(N,d)$ plane. Below $d_{DR}(N)$, our formalism gives access to both the typical behavior of the system, controlled by zero-temperature fixed points with a nonanalytic dimensionless effective action, and to the physics of rare low-energy excitations ("droplets"), described at nonzero temperature by the rounding of the nonanalyticity in a thermal boundary layer.
Tarjus Gilles
Tissier Matthieu
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