Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The fate of $O(N)$ multi-critical universal behaviour   The multi-critical fixed points of $O(N)$ symmetric models cease to exist in
the $N\to\infty$ limit, but the mechanism regulating their annihilation still
presents several enigmatic aspects. Here, we explore the evolution of
high-order multi-critical points in the $(d,N)$ plane and uncover a complex
mosaics for their asymptotic behaviour at large $N$. This picture is confirmed
by various RG approaches and constitutes a fundamental step towards the full
comprehension of critical behaviour in $O(N)$ field theories.

22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int