Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effects of Two Energy Scales in Weakly Dimerized Antiferromagnetic
  Quantum Spin Chains   By means of thermal expansion and specific heat measurements on the
high-pressure phase of (VO)$_2$P$_2$O$_7$, the effects of two energy scales of
the weakly dimerized antiferromagnetic $S$ = 1/2 Heisenberg chain are explored.
The low energy scale, given by the spin gap $\Delta$, is found to manifest
itself in a pronounced thermal expansion anomaly. A quantitative analysis,
employing T-DMRG calculations, shows that this feature originates from changes
in the magnetic entropy with respect to $\Delta$, $\partial S^{m}/ \partial
\Delta$. This term, inaccessible by specific heat, is visible only in the
weak-dimerization limit where it reflects peculiarities of the excitation
spectrum and its sensitivity to variations in $\Delta$.

1
The categories of this paper are: cs
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: eess
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
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The categories of this paper are: nlin
21
The categories of this paper are: adap-org
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The categories of this paper are: stat
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg