Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical
  Models   The lower-critical dimension for the existence of the Ising spin-glass phase
is calculated, numerically exactly, as $d_L = 2.520$ for a family of
hierarchical lattices, from an essentially exact (correlation coefficent $R^2 =
0.999999$) near-linear fit to 23 different diminishing fractional dimensions.
To obtain this result, the phase transition temperature between the disordered
and spin-glass phases, the corresponding critical exponent $y_T$, and the
runaway exponent $y_R$ of the spin-glass phase are calculated for consecutive
hierarchical lattices as dimension is lowered.

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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
2
The categories of this paper are: math
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin