Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High q-State Clock Spin Glasses in Three Dimensions and the Lyapunov
  Exponents of Chaotic Phases and Chaotic Phase Boundaries   Spin-glass phases and phase transitions for q-state clock models and their q
$\rightarrow \infty$ limit the XY model, in spatial dimension d=3, are studied
by a detailed renormalization-group study that is exact for the d=3
hierarchical lattice and approximate for the cubic lattice. In addition to the
now well-established chaotic rescaling behavior of the spin-glass phase, each
of the two types of spin-glass phase boundaries displays, under
renormalization-group trajectories, their own distinctive chaotic behavior.
These chaotic renormalization-group trajectories subdivide into two categories,
namely as strong-coupling chaos (in the spin-glass phase and, distinctly, on
the spinglass-ferromagnetic phase boundary) and as intermediate-coupling chaos
(on the spinglass-paramagnetic phase boundary). We thus characterize each
different phase and phase boundary exhibiting chaos by its distinct Lyapunov
exponent, which we calculate. We show that, under renormalization-group,
chaotic trajectories and fixed distributions are mechanistically and
quantitatively equivalent. The phase diagrams of arbitrary even q-state clock
spin-glass models in d=3 are calculated. These models, for all non-infinite q,
have a finite-temperature spin-glass phase. Furthermore, the spin-glass phases
exhibit a universal ordering behavior, independent of q. The spin-glass phases
and the spinglass-paramagnetic phase boundaries exhibit universal fixed
distributions, chaotic trajectories and Lyapunov exponents. In the XY model
limit, our calculations indicate a zero-temperature spin-glass phase.

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The categories of this paper are: atom-ph
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph