Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical $1$- and $2$-point spin correlations for the $O(2)$ model in
  $3d$ bounded domains   We study the critical properties of the $3d$ $O(2)$ universality class in
bounded domains through Monte Carlo simulations of the clock model. We use an
improved version of the latter, chosen to minimize finite-size corrections at
criticality, with 8 orientations of the spins and in the presence of vacancies.
The domain chosen for the simulations is the slab configuration with fixed
spins at the boundaries. We obtain the universal critical magnetization profile
and two-point correlations, which favorably compare with the predictions of the
critical geometry approach based on the Yamabe equation. The main result is
that the correlations, once the dimensionful contributions are factored out
with the critical magnetization profile, are shown to only depend on the
distance between the points computed using a metric found solving the
fractional Yamabe equation. The quantitative comparison with the corresponding
results for the Ising model at criticality is shown and discussed. Moreover,
from the magnetization profiles the critical exponent $\eta$ is extracted and
found to be in reasonable agreement with up-to-date results.

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th