Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random-field Ising and $O(N)$ models: Theoretical description through
  the functional renormalization group   We review the theoretical description of the random field Ising and $O(N)$
models obtained from the functional renormalization group, either in its
nonperturbative implementation or, in some limits, in perturbative
implementations. The approach solves some of the questions concerning the
critical behavior of random-field systems that have stayed pending for many
years: What is the mechanism for the breakdown of dimensional reduction and the
breaking of the underlying supersymmetry below $d=6$? Can one provide a
theoretical computation of the critical exponents, including the exponent \psi
characterizing the activated dynamic scaling? Is it possible to theoretically
describe collective phenomena such as avalanches and droplets? Is the critical
scaling described by 2 or 3 independent exponents? What is the phase behavior
of the random-field $O(N)$ model in the whole ($N$, $d$) plane and what is the
lower critical dimension of quasi-long range order for $N=2$? Are the
equilibrium and out-of-equilibrium critical points of the RFIM in the same
universality class?

36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an