Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry breaking in two-dimensional square grids: persistence and
  failure of the dimensional crossover   We discuss the model robustness of the infinite two-dimensional square grid
with respect to symmetry breakings due to the presence of defects, that is,
lacks of finitely or infinitely many edges. Precisely, we study how these
topological perturbations of the square grid affect the so-called dimensional
crossover identified in [Adami et al. 2019]. Such a phenomenon has two
evidences: the coexistence of the one and the two-dimensional Sobolev
inequalities and the appearence of a continuum of $L^2$-critical exponents for
the ground states at fixed mass of the nonlinear Schr\"odinger equation. From
this twofold perspective, we investigate which classes of defects do preserve
the dimensional crossover and which classes do not.

10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int