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

Matthieu Tissier, Gilles Tarjus
2008 Physical Review B  
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
more » ... ves 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.
doi:10.1103/physrevb.78.024204 fatcat:gimnxhandzelrd6mouzql6ywre