Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phase transition for loop representations of Quantum spin systems on
  trees   We consider a model of random loops on Galton-Watson trees with an offspring
distribution with high expectation. We give the configurations a weighting of
$\theta^{\#\text{loops}}$. For many $\theta>1$ these models are equivalent to
certain quantum spin systems for various choices of the system parameters. We
find conditions on the offspring distribution that guarantee the occurrence of
a phase transition from finite to infinite loops for the Galton-Watson tree.

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The categories of this paper are: funct-an
3
The categories of this paper are: physics
1
The categories of this paper are: cs
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex