Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The
  Role of Cusps in the Fixed Point Potentials   The large $N$ expansion plays a fundamental role in quantum and statistical
field theory. We show on the example of the O$(N)$ model that at $N=\infty$,
its traditional implementation misses in all dimensions below four some fixed
points of the renormalization group. These new fixed points show singularities
at $N=\infty$ in their effective potential that become a boundary layer at
finite $N$. We show that they have a physical impact on the multicritcal
physics of the $O(N$) model at finite $N$. We also show that the mechanism at
play holds also for the O($N$)$\otimes$O(2) model and is thus probably generic.

31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol