Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monte Carlo studies of the ordering of the one-dimensional Heisenberg
  spin glass with long-range power-law interactions   The nature of the ordering of the one-dimensional Heisenberg spin-glass model
with a long-range power-law interaction is studied by extensive Monte Carlo
simulations, with particular attention to the issue of the spin-chirality
decoupling/coupling. Large system sizes up to $L=4096$ are studied. With
varying the exponent $\sigma$ describing the power-law interaction, we observe
three distinct types of ordering regimes. For smaller $\sigma$, the spin and
the chirality order at a common finite temperature with a common
correlation-length exponent, exhibiting the standard spin-chirality coupling
behavior. For intermediate $\sigma$, the chirality orders at a temperature
higher than the spin, exhibiting the spin-chirality decoupling behavior. For
larger $\sigma$, both the spin and the chirality order at zero temperature. We
construct a phase diagram in the $\sigma$ versus the temperature plane, and
discuss implications of the results. Critical properties associated with both
the chiral-glass and the spin-glass transitions are also determined.

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The categories of this paper are: q-bio
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The categories of this paper are: econ
25
The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph