Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Field-Induced Ising Criticality and Incommensurability in Anisotropic
  Spin-1 Chains   Quantum phase transitions induced by an external magnetic field in the
Haldane-gapped spin-1 chains are studied in a fermionic field-theoretic
description of the model. In the case with broken axial symmetry, two
transitions occurs consecutively as increasing the field: $h_c=(m_1 m_2)^{1/2}$
(with $m_1$ and $m_2$ the transverse masses) is the critical Ising point and
$\tilde{h}_c^* (> h_c)$ is the commensurate-incommensurate transition point.
Although the latter is thermodynamically indiscernible, its property is
revealed in the spin correlation functions (both uniform and staggered) which
are calculated upon expressing the correlations of coupled Ising pair fields in
terms of block-Toeplitz determinants.

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The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: physics
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
25
The categories of this paper are: patt-sol