Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\mathbb{Z}_4$-symmetric perturbations to the XY model from functional
  renormalization   We employ the second order of the derivative expansion of the nonperturbative
renormalization group to study cubic ($\mathbb{Z}_4$-symmetric) perturbations
to the classical $XY$ model in dimensionality $d\in [2,4]$. In $d=3$ we provide
accurate estimates of the eigenvalue $y_4$ corresponding to the leading
irrelevant perturbation and follow the evolution of the physical picture upon
reducing spatial dimensionality from $d=3$ towards $d=2$, where we
approximately recover the onset of the Kosterlitz-Thouless physics. We analyze
the interplay between the leading irrelevant eigenvalues related to
$O(2)$-symmetric and $\mathbb{Z}_4$-symmetric perturbations and their
approximate collapse for $d\to 2$. We compare and discuss different
implementations of the derivative expansion in cases involving one and two
invariants of the corresponding symmetry group.

32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th