Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third and Fourth Order Phase Transitions: Exact Solution for the Ising
  Model on the Cayley Tree   An exact analytical derivation is presented, showing that the Ising model on
the Cayley tree exhibits a line of third order phase transition points, between
temperatures $T_2=2k_B^{-1}J\ln ({\sqrt 2}+1) $ and $T_{BP}=k_B^{-1}J\ln (3)$,
and a line of fourth order phase transitions between $T_{BP}$ and $\infty$,
where $k_B$ is the Boltzmann constant, and $J$ is the nearest-neighbor
interaction parameter.

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The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin