Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forest expansion of two-body partition functions for sparse interaction
  graphs   We study tree approximations to classical two-body partition functions on
sparse and loopy graphs via the Brydges-Kennedy-Abdessalam-Rivasseau forest
expansion. We show that for sparse graphs (with large cycles), the partition
function above a certain temperature $T^*$ can be approximated by a graph
polynomial expansion over forests of the interaction graph. Within this "forest
phase", we show that the approximation can be written in terms of a reference
tree $\mathcal T$ on the interaction graph, with corrections due to cycles.
From this point of view, this implies that high-temperature models are easy to
solve on sparse graphs, as one can evaluate the partition function using belief
propagation. We also show that there exists a high- and low-temperature regime,
in which $\mathcal T$ can be obtained via a maximal spanning tree algorithm on
a (given) weighted graph. We study the algebra of these corrections and provide
first- and second-order approximation to the tree Ansatz, and give explicit
examples for the first-order approximation.

8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an