Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. II: Results for the Random Field O(N) Model

TL;DR

This paper uses a nonperturbative functional renormalization group approach to analyze the critical behavior, phase diagram, and ordering phenomena of the random field O(N) model across different dimensions and N values.

Contribution

It provides a comprehensive analysis of the breakdown of dimensional reduction and describes criticality and ordering in the entire (N,d) parameter space using a novel nonperturbative method.

Findings

Dimensional reduction breaks down below a critical dimension d_{DR}(N).

The formalism captures zero-temperature fixed points with nonanalytic effective actions.

It describes the physics of rare low-energy excitations ('droplets') at nonzero temperature.

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, 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.