Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On monotonicity and couplings of random currents and the
  loop-$\mathrm{O}(1)$-model   Using recent couplings we provide counterexamples to monotonicity properties
of percolation models related to graphical representations of the Ising model.
We further prove a new coupling of the double random current model to the
loop-$\mathrm{O}(1)$-model.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs